https://apcz.umk.pl/TMNA/issue/feedTopological Methods in Nonlinear Analysis2022-12-31T00:00:00+01:00Wojciech Kryszewskitmna@ncu.plOpen Journal Systems<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>https://apcz.umk.pl/TMNA/article/view/39985Global existence, local existence and blow-up of mild solutions for abstract time-space fractional diffusion equations2022-09-13T21:55:47+02:00Yongqiang Futmna@ncu.plXiaoju Zhangxiaoxiaojuzhang@126.comIn 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.2022-09-13T00:00:00+02:00Copyright (c) 2022 Yongqiang Fu, Xiaoju Zhanghttps://apcz.umk.pl/TMNA/article/view/39773Realization of rotation vectors for volume preserving homeomorphisms of the torus2022-09-04T16:48:28+02:00Paulo Varandaspaulo.varandas@ufba.brIn 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 $\text{Homeo}_{0,\lambda}(\mathbb T^m)$.2022-08-31T00:00:00+02:00Copyright (c) 2022 Paulo Varandashttps://apcz.umk.pl/TMNA/article/view/41317An accelerated variant of the projection based parallel hybrid algorithm for split null point problems2022-12-10T00:01:39+01:00Yasir Arfatyasir.arfat@mail.kmutt.ac.thPoom Kumampoom.kum@kmutt.ac.thMuhammad Aqeel Ahmad Khanitsakb@hotmail.comParinya Sa Ngiamsunthornparinya.san@kmutt.ac.thIn 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.2022-12-10T00:00:00+01:00Copyright (c) 2022 Yasir Arfat, Poom Kumam, Muhammad Aqeel Ahmad Khan, Parinya Sa Ngiamsunthornhttps://apcz.umk.pl/TMNA/article/view/40184Absolute normalized norms in R^2 and Heinz means constant2022-09-24T19:47:14+02:00Zhan-fei Zuozuozhanfei@139.comYi-min Huangtmna@ncu.plIn 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.2022-09-24T00:00:00+02:00Copyright (c) 2022 Zhan-fei Zuo, Yi-min Huanghttps://apcz.umk.pl/TMNA/article/view/39786The Borsuk-Ulam property for homotopy classes of maps from the torus to the Klein bottle - part 22022-09-04T16:48:29+02:00Daciberg Lima Gonçalvesdlgoncal@ime.usp.brJohn Guaschijohn.guaschi@unicaen.frVinicius Casteluber Laassvinicius.laass@ufba.brLet $M$ 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 $\mathbb{T}^2$.2022-08-31T00:00:00+02:00Copyright (c) 2022 Daciberg Lima Gonçalves, John Guaschi, Vinicius Casteluber Laasshttps://apcz.umk.pl/TMNA/article/view/41315Existence results for fractional Brezis-Nirenberg type problems in unbounded domains2022-12-10T00:01:38+01:00Yansheng Shenysshen@mail.bnu.edu.cnXumin Wangxmwang@bjfu.edu.cnIn 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.2022-12-10T00:00:00+01:00Copyright (c) 2022 Yansheng Shen, Xumin Wanghttps://apcz.umk.pl/TMNA/article/view/41095Regularization methods for solving the split feasibility problem with multiple output sets in Hilbert spaces2022-11-29T20:33:24+01:00Simeon Reichsreich@technion.ac.ilTruong Minh Tuyentuyentm@tnus.edu.vnWe 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.2022-11-29T00:00:00+01:00Copyright (c) 2022 Simeon Reich, Truong Minh Tuyenhttps://apcz.umk.pl/TMNA/article/view/41316A note on local minimizers of energy on complete manifolds2022-12-10T00:01:39+01:00Márcio Batistamhbs@mat.ufal.brJosé I. Santosjissivan@gmail.comIn 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.2022-12-10T00:00:00+01:00Copyright (c) 2022 Márcio Batista, José I. Santoshttps://apcz.umk.pl/TMNA/article/view/41351Fourth-order elliptic problems involving concave-superlinear nonlinearities2022-12-11T13:44:32+01:00Thiago R. Cavalcantethiago.cavalcante@uft.edu.brEdcarlos D. Silvaedcarlos@ufg.brThe 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.2022-12-11T00:00:00+01:00Copyright (c) 2022 Thiago R. Cavalcante, Edcarlos D. Silvahttps://apcz.umk.pl/TMNA/article/view/41319A-priori bound and Hölder continuity of solutions to degenerate elliptic equations with variable exponents2022-12-10T00:01:39+01:00Ky Hokyhn@ueh.edu.vnLe Cong Nhannhanlc@hcmute.edu.vnLe Xuan Truonglxuantruong@gmail.comWe 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.2022-12-10T00:00:00+01:00Copyright (c) 2022 Ky Ho, Le Cong Nhan, Le Xuan Truonghttps://apcz.umk.pl/TMNA/article/view/41318Periodic solutions of fractional Laplace equations: Least period, axial symmetry and limit2022-12-10T00:01:39+01:00Zhenping Fengfengzp@hnu.edu.cnZhuoran Duduzr@hnu.edu.cnWe 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 $T\rightarrow+\infty$.2022-12-10T00:00:00+01:00Copyright (c) 2022 Zhenping Feng, Zhuoran Duhttps://apcz.umk.pl/TMNA/article/view/41320Time-dependent global attractors for the strongly damped wave equations with lower regular forcing term2022-12-10T00:01:40+01:00Xinyu Meimeixy@szu.edu.cnTao Sunsuntao5771@163.comYongqin Xiexieyq@csust.edu.cnKaixuan Zhuzhukx12@163.comIn 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.2022-12-10T00:00:00+01:00Copyright (c) 2022 Xinyu Mei, Tao Sun, Yongqin Xie, Kaixuan Zhuhttps://apcz.umk.pl/TMNA/article/view/41321Some existence results for elliptic systems with exponential nonlinearities and convection terms in dimension two2022-12-10T00:01:40+01:00Wei Liu63525138@qq.comIn 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}.2022-12-10T00:00:00+01:00Copyright (c) 2022 Wei Liuhttps://apcz.umk.pl/TMNA/article/view/41352On radial solutions for some elliptic equations involving operators with unbounded coefficients in exterior domains2022-12-11T13:44:34+01:00Anderson L. A. de Araujoanderson.araujo@ufv.brLuiz F.O. Farialuiz.faria@ufjf.edu.brSalomón Alarcónsalomon.alarcon@usm.clLeonelo Iturriagaleonelo.iturriaga@usm.cl 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.2022-12-11T00:00:00+01:00Copyright (c) 2022 Anderson L. A. de Araujo, Luiz F.O. Faria, Salomón Alarcón, Leonelo Iturriagahttps://apcz.umk.pl/TMNA/article/view/41322Affine-periodic solutions for generalized ODEs and other equations2022-12-10T00:01:40+01:00Márcia Federsonfederson@icmc.usp.brRogelio Graurogeliograu@gmail.comCarolina Mesquitamc12stefani@hotmail.comIt 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.2022-12-10T00:00:00+01:00Copyright (c) 2022 Márcia Federson, Rogelio Grau, Carolina Mesquitahttps://apcz.umk.pl/TMNA/article/view/41323On a semilinear fourth order elliptic problem with asymmetric nonlinearity2022-12-10T00:01:40+01:00Fabiana Ferreirafabiana.m.ferreira@ufes.brEveraldo S. Medeiroseveraldo@mat.ufpb.brWallisom Rosawallisom@ufu.brIn 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.2022-12-10T00:00:00+01:00Copyright (c) 2022 Fabiana Ferreira, Everaldo S. Medeiros, Wallisom Rosa