Topological Methods in Nonlinear Analysis
https://apcz.umk.pl/TMNA
<p><span style="font-size: 12px;"><a href="https://www.tmna.ncu.pl/">TMNA</a> publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those which employ topological methods. Papers in topology which are of intereset in nonlinear problems may also be included.</span></p> <p><span style="font-size: 12px;">The current impact factor is <strong>IF 2021 = <strong id="yui_patched_v3_11_0_1_1578693261971_720">0.869</strong></strong><strong style="font-size: 12px;">.</strong></span></p> <p> </p> <p><span style="font-size: 12px;">The project "Digital service and digitization of the resources of the journal <a href="https://www.tmna.ncu.pl/">Topological Methods in Nonlinear Analysis</a>” including the digital service for the volumes 53 (2019) and 54 (2019) has been funded by the Ministry of Science and Higher Education as a part of the 623/P-DUN/2018 agreement. </span></p> <p><img src="https://apcz.umk.pl/czasopisma/public/site/images/tmna/mnisw.jpg" alt="MNiSW" width="300/" /></p>en-UStmna@ncu.pl (Wojciech Kryszewski)tmna@ncu.pl (Mariusz Czerniak)Sat, 31 Dec 2022 00:00:00 +0100OJS 3.3.0.14http://blogs.law.harvard.edu/tech/rss60Global existence, local existence and blow-up of mild solutions for abstract time-space fractional diffusion equations
https://apcz.umk.pl/TMNA/article/view/39985
In this paper, we consider initial boundary value problems for abstract fractional diffusion equations $\partial_{t}^{\beta}u+(-\Delta)^{s}u=g(t,x,u)$ with the Caputo time fractional derivatives and fractional Laplacian operators. When $g(t,x,u)$ satisfies condition (G), problems can be applied by a strong maximum principle involving time-space fractional derivatives. Hence, we establish the global existence and uniqueness of mild solution by upper and lower solutions method. Moreover, the mild solution mentioned above turns out to be a classical solution. When condition (G) does not hold, then we study nonexistence of global solutions under certain conditions, and we obtain the local existence and blow-up of mild solutions. Further, we conclude that the first eigenvalue $\lambda_1$ seems to be a critical value for nonlinear problems.Yongqiang Fu, Xiaoju Zhang
Copyright (c) 2022 Yongqiang Fu, Xiaoju Zhang
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https://apcz.umk.pl/TMNA/article/view/39985Tue, 13 Sep 2022 00:00:00 +0200Realization of rotation vectors for volume preserving homeomorphisms of the torus
https://apcz.umk.pl/TMNA/article/view/39773
In this note we study the level sets of rotation vectors for $C^0$-generic homeomorphisms in the space $\text{Homeo}_{0,\lambda}(\mathbb T^m)$ $(m \geq 3)$ of volume preserving homeomorphisms isotopic to the identity, and contribute to the ergodic optimization of vector valued observables. It is known that such homeomorphisms satisfy the specification property and their rotation sets are polyhedrons with rational vertices and non-empty interior, and stable \cite{BLV}, \cite{GL}, \cite{LV}. For a $C^0$-generic homeomorphism we prove uniform bounded deviations for the displacement of points in $\mathbb T^m$ in the support of any ergodic probability that generates a rotation vector in the boundary of the rotation set. As consequences, we show: (i) the support of ergodic probabilities generating rotation vectors in the boundary of rotation sets has empty interior, and (ii) weak version of Boyland's conjecture: the rotation vector of the Lebesgue measure lies in the interior of the rotation sets for a $C^0$-open and dense subset of homeomorphisms in $\text{Homeo}_{0,\lambda}(\mathbb T^m)$.Paulo Varandas
Copyright (c) 2022 Paulo Varandas
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https://apcz.umk.pl/TMNA/article/view/39773Wed, 31 Aug 2022 00:00:00 +0200An accelerated variant of the projection based parallel hybrid algorithm for split null point problems
https://apcz.umk.pl/TMNA/article/view/41317
In this paper, we consider an accelerated shrinking projection based parallel hybrid algorithm to study the split null point problem (SNPP) associated with the maximal monotone operators in Hilbert spaces. The analysis of the proposed algorithm provides strong convergence results under suitable set of control conditions as well as viability with the help of a numerical experiment. The results presented in this paper improve various existing results in the current literature.Yasir Arfat, Poom Kumam, Muhammad Aqeel Ahmad Khan, Parinya Sa Ngiamsunthorn
Copyright (c) 2022 Yasir Arfat, Poom Kumam, Muhammad Aqeel Ahmad Khan, Parinya Sa Ngiamsunthorn
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https://apcz.umk.pl/TMNA/article/view/41317Sat, 10 Dec 2022 00:00:00 +0100Absolute normalized norms in R^2 and Heinz means constant
https://apcz.umk.pl/TMNA/article/view/40184
In this paper, we calculate the precise values of the Heinz means constant under the absolute normalized norms in $\mathbb{R}^2$. The conclusions do not only contain some previous results, but also give the exact values of the Heinz means constant for some new concrete Banach spaces.Zhan-fei Zuo, Yi-min Huang
Copyright (c) 2022 Zhan-fei Zuo, Yi-min Huang
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https://apcz.umk.pl/TMNA/article/view/40184Sat, 24 Sep 2022 00:00:00 +0200The Borsuk-Ulam property for homotopy classes of maps from the torus to the Klein bottle - part 2
https://apcz.umk.pl/TMNA/article/view/39786
Let $M$ be a topological space that admits a free involution $\tau$, and let $N$ be a topological space. A homotopy class $\beta \in [ M,N ]$ is said to have {\it the Borsuk-Ulam property with respect to $\tau$} if for every representative map $f\colon M\to N$ of $\beta$, there exists a point $x \in M$ such that $f(\tau(x))= f(x)$. In this paper, we determine the homotopy class of maps from the $2$-torus $\mathbb{T}^2$ to the Klein bottle $\mathbb{K}^2$ that possess the Borsuk-Ulam property with respect to any free involution of $\mathbb{T}^2$ for which the orbit space is $\mathbb{K}^2$. Our results are given in terms of a certain family of homomorphisms involving the fundamental groups of $\mathbb{T}^2$ and $\mathbb{K}^2$. This completes the analysis of the Borsuk-Ulam problem for the case $M=\mathbb{T}^2$ and $N=\mathbb{K}^2$, and for any free involution $\tau$ of $\mathbb{T}^2$.Daciberg Lima Gonçalves, John Guaschi, Vinicius Casteluber Laass
Copyright (c) 2022 Daciberg Lima Gonçalves, John Guaschi, Vinicius Casteluber Laass
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https://apcz.umk.pl/TMNA/article/view/39786Wed, 31 Aug 2022 00:00:00 +0200Existence results for fractional Brezis-Nirenberg type problems in unbounded domains
https://apcz.umk.pl/TMNA/article/view/41315
In this paper we study the fractional Brezis-Nirenberg type problems in unbounded cylinder-type domains \begin{align*} \begin{cases} (-\Delta)^{s}u-\mu\dfrac{u}{|x|^{2s}}=\lambda u+|u|^{2^{\ast}_{s}-2}u & \text{in } \Omega,\\ u=0 & \text{in } \mathbb{R}^{N}\setminus \Omega, \end{cases} \end{align*} where $(-\Delta)^{s}$ is the fractional Laplace operator with $s\in(0,1)$, $\mu\in[0,\Lambda_{N,s})$ with $\Lambda_{N,s}$ the best fractional Hardy constant, $\lambda> 0$, $N> 2s$ and $2^{\ast}_{s}={2N}/({N-2s})$ denotes the fractional critical Sobolev exponent. By applying the fractional Poincaré inequality together with the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove an existence result to the equation.Yansheng Shen, Xumin Wang
Copyright (c) 2022 Yansheng Shen, Xumin Wang
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https://apcz.umk.pl/TMNA/article/view/41315Sat, 10 Dec 2022 00:00:00 +0100Regularization methods for solving the split feasibility problem with multiple output sets in Hilbert spaces
https://apcz.umk.pl/TMNA/article/view/41095
We study the split feasibility problem with multiple output sets in Hilbert spaces. In order to solve this problem, we introduce several new iterative processes by using the Tikhonov regularization method.Simeon Reich, Truong Minh Tuyen
Copyright (c) 2022 Simeon Reich, Truong Minh Tuyen
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https://apcz.umk.pl/TMNA/article/view/41095Tue, 29 Nov 2022 00:00:00 +0100A note on local minimizers of energy on complete manifolds
https://apcz.umk.pl/TMNA/article/view/41316
In this paper, we study the geometric rigidity of complete Riemannian manifolds admitting local minimizers of energy functionals. More precisely, assuming the existence of a non-trivial local minimizer and under suitable assumptions, a Riemannian manifold under consideration must be a product manifold furnished with a warped metric. Secondly, under similar hypotheses, we deduce a geometrical splitting in the same fashion as in the Cheeger-Gromoll splitting theorem and we also get information about local minimizers.Márcio Batista, José I. Santos
Copyright (c) 2022 Márcio Batista, José I. Santos
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https://apcz.umk.pl/TMNA/article/view/41316Sat, 10 Dec 2022 00:00:00 +0100Fourth-order elliptic problems involving concave-superlinear nonlinearities
https://apcz.umk.pl/TMNA/article/view/41351
The existence of solutions for a huge class of superlinear elliptic problems involving fourth-order elliptic problems defined on bounded domains under Navier boundary conditions is established. To this end we do not apply the well-known Ambrosetti-Rabinowitz condition. Instead, we assume that the nonlinear term is nonquadratic at infinity. Furthermore, the nonlinear term is a concave-superlinear function which can be indefinite in sign. In order to apply variational methods we employ some delicate arguments recovering some kind of compactness.Thiago R. Cavalcante, Edcarlos D. Silva
Copyright (c) 2022 Thiago R. Cavalcante, Edcarlos D. Silva
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https://apcz.umk.pl/TMNA/article/view/41351Sun, 11 Dec 2022 00:00:00 +0100A-priori bound and Hölder continuity of solutions to degenerate elliptic equations with variable exponents
https://apcz.umk.pl/TMNA/article/view/41319
We investigate the boundedness and regularity of solutions to degenerate elliptic equations with variable exponents that are subject to the Dirichlet boundary condition. By employing the De Giorgi iteration, we obtain a-priori bounds and the Hölder continuity for solutions. As an application, we obtain the existence of infinitely many small solutions for a class of degenerate elliptic equations involving variable exponents.Ky Ho, Le Cong Nhan, Le Xuan Truong
Copyright (c) 2022 Ky Ho, Le Cong Nhan, Le Xuan Truong
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https://apcz.umk.pl/TMNA/article/view/41319Sat, 10 Dec 2022 00:00:00 +0100Periodic solutions of fractional Laplace equations: Least period, axial symmetry and limit
https://apcz.umk.pl/TMNA/article/view/41318
We are concerned with periodic solutions of the fractional Laplace equation \begin{equation*} {(-\partial_{xx})^s}u(x)+F'(u(x))=0 \quad \mbox{in }\mathbb{R}, \end{equation*} where $0< s< 1$. The smooth function $F$ is a double-well potential with wells at $+1$ and $-1$. We show that the value of least positive period is $2{\pi}\times({1}/{-F''(0)})^{{1}/({2s})}$. The axial symmetry of odd periodic solutions is obtained by moving plane method. We also prove that odd periodic solutions $u_{T}(x)$ converge to a layer solution of the same equation as periods $T\rightarrow+\infty$.Zhenping Feng, Zhuoran Du
Copyright (c) 2022 Zhenping Feng, Zhuoran Du
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https://apcz.umk.pl/TMNA/article/view/41318Sat, 10 Dec 2022 00:00:00 +0100Time-dependent global attractors for the strongly damped wave equations with lower regular forcing term
https://apcz.umk.pl/TMNA/article/view/41320
In this paper, based on a new theoretical framework of time-dependent global attractors (Conti, Pata and Temam \cite{CPT13}), we consider the strongly damped wave equations $\varepsilon(t)u_{tt}-\Delta u_{t}-\Delta u+f(u)=g(x)$ and establish the existence of attractors in $\mathcal{H}_{t}=H_{0}^{1}(\Omega)\times L^{2}(\Omega)$ and $\mathcal{V}_{t}=H_{0}^{1}(\Omega)\times H_{0}^{1}(\Omega)$, respectively.Xinyu Mei, Tao Sun, Yongqin Xie, Kaixuan Zhu
Copyright (c) 2022 Xinyu Mei, Tao Sun, Yongqin Xie, Kaixuan Zhu
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https://apcz.umk.pl/TMNA/article/view/41320Sat, 10 Dec 2022 00:00:00 +0100Some existence results for elliptic systems with exponential nonlinearities and convection terms in dimension two
https://apcz.umk.pl/TMNA/article/view/41321
In this paper, we establish the existence of solutions to a class of elliptic systems. The nonlinearities include exponential growth terms and convection terms. The exponential growth term means it could be critical growth at $\infty$. The Trudinger-Moser inequality is used to deal with it. The convection term means it involves the gradient of unknown function. The strong convergence of sequences is employed to overcome the difficulties caused by convection terms. The variational methods are invalid and the Galerkin method and an approximation scheme are applied to obtain four different solutions. Our results supplements those from \cite{Araujo2018}.Wei Liu
Copyright (c) 2022 Wei Liu
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https://apcz.umk.pl/TMNA/article/view/41321Sat, 10 Dec 2022 00:00:00 +0100On radial solutions for some elliptic equations involving operators with unbounded coefficients in exterior domains
https://apcz.umk.pl/TMNA/article/view/41352
We study existence and multiplicity of radial solutions for some quasilinear elliptic problems involving the operator $L_N=\Delta - x\cdot \nabla$ on $\mathbb{R}^N\setminus B_1$, where $\Delta$ is the Laplacian, $x\cdot \nabla$ is an unbounded drift term, $N\geq 3$ and $B_1$ is the unit ball centered at the origin. We consider: (i) Eigenvalue problems, and (ii) Problems involving a nonlinearity of concave and convex type. On the first class of problems we get a compact embedding result, whereas on the second, we address the well-known question of Ambrosetti, Brezis and Cerami from 1993 concerning the existence of two positive solutions for some problems involving the supercritical Sobolev exponent in symmetric domains for the Laplacian. Specifically, we provide\linebreak a new approach of answering the ABC-question for elliptic problems with unbounded coefficients in exterior domains and we find asymptotic properties of the radial solutions. Furthermore, we study the limit case, namely when nonlinearity involves a sublinear term and a linear term. As far as we know, this is the first work that deals with such a case, even for the Laplacian. In our approach, we use both topological and variational arguments.Anderson L. A. de Araujo, Luiz F.O. Faria, Salomón Alarcón, Leonelo Iturriaga
Copyright (c) 2022 Anderson L. A. de Araujo, Luiz F.O. Faria, Salomón Alarcón, Leonelo Iturriaga
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https://apcz.umk.pl/TMNA/article/view/41352Sun, 11 Dec 2022 00:00:00 +0100Affine-periodic solutions for generalized ODEs and other equations
https://apcz.umk.pl/TMNA/article/view/41322
It is known that the concept of affine-periodicity encompasses classic notions of symmetries as the classic periodicity, anti-periodicity and rotating symmetries (in particular, quasi-periodicity). The aim of this paper is to establish the basis of affine-periodic solutions of generalized ODEs. Thus, for a given real number $T> 0$ and an invertible $n\times n$ matrix $Q$, with entries in $\mathbb C$, we establish conditions for the existence of a $(Q,T)$-affine-periodic solution within the framework of nonautonomous generalized ODEs, whose integral form displays the nonabsolute Kurzweil integral, which encompasses many types of integrals, such as the Riemann, the Lebesgue integral, among others. The main tools employed here are the fixed point theorems of Banach and of Krasnosel'skiĭ. We apply our main results to measure differential equations with Henstock-Kurzweil-Stiejtes righthand sides as well as to impulsive differential equations and dynamic equations on time scales which are particular cases of the former.Márcia Federson, Rogelio Grau, Carolina Mesquita
Copyright (c) 2022 Márcia Federson, Rogelio Grau, Carolina Mesquita
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https://apcz.umk.pl/TMNA/article/view/41322Sat, 10 Dec 2022 00:00:00 +0100On a semilinear fourth order elliptic problem with asymmetric nonlinearity
https://apcz.umk.pl/TMNA/article/view/41323
In this work, we address the existence of solutions for a biharmonic elliptic equation with homogeneous Navier boundary condition. The problem is asymmetric and has linear behavior on $-\infty$ and superlinear on $+\infty$. To obtain the results we apply topological methods.Fabiana Ferreira, Everaldo S. Medeiros, Wallisom Rosa
Copyright (c) 2022 Fabiana Ferreira, Everaldo S. Medeiros, Wallisom Rosa
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https://apcz.umk.pl/TMNA/article/view/41323Sat, 10 Dec 2022 00:00:00 +0100