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 interest in nonlinear problems may also be included.</span></p> <p><span style="font-size: 12px;"><strong>Journal Metrics</strong></span></p> <table width="400"> <tbody> <tr> <td><span style="font-size: 12px;">CiteScore</span></td> <td><span style="font-size: 12px;">2022</span></td> <td><span style="font-size: 12px;">1.2</span></td> </tr> <tr> <td><span style="font-size: 12px;">Impact Factor</span></td> <td><span style="font-size: 12px;">2022</span></td> <td><span style="font-size: 12px;">0.700</span></td> </tr> <tr> <td><span style="font-size: 12px;">5-Year Impact Factor</span></td> <td><span style="font-size: 12px;">2021</span></td> <td><span style="font-size: 12px;">0.978</span></td> </tr> <tr> <td><span style="font-size: 12px;">AIS</span></td> <td><span style="font-size: 12px;">2021</span></td> <td><span style="font-size: 12px;">0.557</span></td> </tr> <tr> <td><span style="font-size: 12px;">SNIP</span></td> <td><span style="font-size: 12px;">2022</span></td> <td><span style="font-size: 12px;">0.826</span></td> </tr> <tr> <td><span style="font-size: 12px;">SJR</span></td> <td><span style="font-size: 12px;">2022</span></td> <td><span style="font-size: 12px;">0.506</span></td> </tr> </tbody> </table> <p> </p> <p><span style="font-size: 12px;">The project "Digital service and digitization of the resources of the journal </span><a style="font-size: 12px; background-color: #ffffff;" href="https://www.tmna.ncu.pl/">Topological Methods in Nonlinear Analysis</a><span style="font-size: 12px;">” 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>Nicolaus Copernicus University in Toruńen-USTopological Methods in Nonlinear Analysis1230-3429Bi-spatial random attractor for stochastic FitzHugh-Nagumo systems on unbounded thin domain
https://apcz.umk.pl/TMNA/article/view/49142
A bi-spatial random attractor is obtained for the stochastic FitzHugh-Nagumo systems on unbounded thin domains when the initial space is $L^2\times L^2$ and the terminate space is $L^p\times L^2$. Furthermore, we establish the upper semi-continuity of attractors under the $p$-norm when a family of $(n+1)$-dimensional thin domains degenerates into a $n$-dimensional unbounded domain.Fuzhi LiDongmei Xu
Copyright (c) 2024 Fuzhi Li, Dongmei Xu
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2024-03-032024-03-0332534710.12775/TMNA.2022.047Normal forms of parabolic logarithmic transseries
https://apcz.umk.pl/TMNA/article/view/52728
We give formal normal forms for parabolic logarithmic transseries $f=z+\dots $, with respect to parabolic logarithmic normalizations. Normalizations are given algorithmically, using fixed point theorems, as limits of Picard's sequences in appropriate complete metric spaces, in contrast to transfinite \emph{term-by-term} eliminations described in former works. Furthermore, we give the explicit formula for the residual coefficient in the normal form and show that, in the larger logarithmic class, we can even eliminate the residual term from the normal form.Dino Peran
Copyright (c) 2024 Dino Peran
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2024-06-162024-06-1634941210.12775/TMNA.2023.039On the operator of center of distances between the spaces of closed subsets of the real line
https://apcz.umk.pl/TMNA/article/view/47721
We study properties of an operator $S$ which assigns to compact subsets of $[0,1]$ their centers of distances. We consider its continuity points and its upper semicontinuity points as well as orbits and fixed points of this operator. We also compute centers of distances of some classic sets. Using properties of operator $S$ we show that the family of achievement sets is of the first category in the space of compact subsets of $[0,1]$.Artur BartoszewiczMałgorzata FilipczakGrażyna HorbaczewskaSebastian LindnerFranciszek Prus-Wiśniowski
Copyright (c) 2023 Artur Bartoszewicz, Małgorzata Filipczak, Grażyna Horbaczewska, Sebastian Lindner, Franciszek Prus-Wiśniowski
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2023-12-312023-12-3141342710.12775/TMNA.2023.023Homogeneous eigenvalue problems in Orlicz-Sobolev spaces
https://apcz.umk.pl/TMNA/article/view/47709
In this article we consider a homogeneous eigenvalue problem ruled by the fractional $g$-Laplacian operator whose Euler-Lagrange equation is obtained by minimization of a quotient involving Luxemburg norms. We prove existence of an infinite sequence of variational eigenvalues and study its behavior as the fractional parameter $s\uparrow 1$ among other stability results.Julián Fernández BonderAriel SalortHernán Vivas
Copyright (c) 2023 Julián Fernández Bonder, Ariel Salort, Hernán Vivas
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2023-12-312023-12-3142945310.12775/TMNA.2023.008On the critical exponents for a fractional diffusion-wave equation with a nonlinear memory term in a bounded domain
https://apcz.umk.pl/TMNA/article/view/49146
In this paper, we prove sharp blow-up and global existence results for a time fractional diffusion-wave equation with a nonlinear memory term in a bounded domain, where the fractional derivative in time is taken in the sense of the Caputo type. Moreover, we also give a result for nonexistence of global solutions to a wave equation with a nonlinear memory term in a bounded domain. The proof of blow-up results is based on the eigenfunction method and the asymptotic properties of solutions for an ordinary fractional differential inequality.Quan-Guo Zhang
Copyright (c) 2024 Quan-Guo Zhang
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2024-03-032024-03-0345548010.12775/TMNA.2023.024Multiplicity and concentration of positive solutions to the double phase Kirchhoff type problems with critical growth
https://apcz.umk.pl/TMNA/article/view/49148
The aim of this paper is to study the multiplicity and concentration of positive solutions to the $(p,q)$ Kirchhoff-type problems involving a positive potential and a continuous nonlinearity with critical growth at infinity. Applying penalization techniques, truncation methods and the Lusternik-Schnirelmann theory, we investigate a relationship between the number of positive solutions and the topology of the set where the potential $V$ attains its minimum values.Jie YangLintao LiuFengjuan Meng
Copyright (c) 2024 Jie Yang, Lintao Liu, Fengjuan Meng
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2024-03-032024-03-0348151310.12775/TMNA.2023.026Normalized solutions to a class of Choquard-type equations with potential
https://apcz.umk.pl/TMNA/article/view/49150
In this paper, we study the existence and nonexistence of solutions to the following Choquard-type equation \begin{equation*} -\Delta u+(V+\lambda)u=(I_\alpha*F(u))f(u)\quad\text{in } \mathbb{R}^N, \end{equation*} having prescribed mass $\int_{\mathbb{R}^N}u^2=a$, where $\lambda\in\mathbb{R}$ will arise as a Lagrange multiplier, $N\geq 3$, $\alpha\in(0,N)$, $I_\alpha$ is Riesz potential. Under suitable assumptions on the potential function $V$ and the nonlinear term $f$, $a_0\in[0,\infty)$ exists such that the above equation has a positive ground state normalized solution if $a\in(a_0,\infty)$ and one has no ground state normalized solution if $a\in(0,a_0)$ when $a_0> 0$ by comparison arguments. Moreover, we obtain sufficient conditions for $a_0=0$.Lei LongXiaojing Feng
Copyright (c) 2024 Lei Long, Xiaojing Feng
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2024-03-032024-03-0351553610.12775/TMNA.2023.028Sectional category of maps related to finite spaces
https://apcz.umk.pl/TMNA/article/view/49151
In this study, we compute some examples of sectional category secat$(f)$ and sectional number sec$(f) for continuous maps $f$ related to finite spaces. Moreover, we introduce an invariant secat$_k(f)$ for a map $f$ between finite spaces using the $k$-th barycentric subdivision and show the equality secat$_k(f)=$ secat$(\mathcal{B}(f))$ for sufficiently large $k$, where $\mathcal{B}(f)$ is the induced map on the associated polyhedra.Kohei Tanaka
Copyright (c) 2024 Kohei Tanaka
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2024-03-032024-03-0353755710.12775/TMNA.2023.029Partial minimization over the Nehari set and applications to elliptic equations
https://apcz.umk.pl/TMNA/article/view/52718
We present a general scheme to find variationally characterized critical points of a functional $I\colon H \to \mathbb{R}$ on a Hilbert space $H$ with hypothesis where the usual Nehari method is not directly applicable. These critical points arise as minima of $I$ over a suitable subset of the associated Nehari set and are obtained with the aid of fibering methods. Moreover, we derive a comparison result with mountain pass critical values. The abstract results will be applied to classes of logarithmic Choquard and nonlinear Schrödinger equations.Omar Cabrera Chavez
Copyright (c) 2024 Omar Cabrera Chavez
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2024-06-162024-06-1655959310.12775/TMNA.2023.031On first and second-order perturbed differential inclusions governed by maximal monotone operators
https://apcz.umk.pl/TMNA/article/view/52719
In this paper we establish, in a separable Hilbert space, a result asserting the existence of absolutely continuous solutions for a system made up of a first-order differential inclusion governed by time and state-dependent maximal monotone operators; and an ordinary differential equation. From this result, we derive existence of absolutely continuous solutions to a second-order differential inclusion governed by time and state-dependent maximal monotone operators.Messaouda BenguessoumDalila Azzam-Laouir
Copyright (c) 2024 Messaouda Benguessoum, Dalila Azzam-Laouir
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2024-06-162024-06-1659561510.12775/TMNA.2023.032Summing multilinear operators and sequence classes
https://apcz.umk.pl/TMNA/article/view/52720
We construct a general framework that generates classes of multilinear operators between Banach spaces which encompasses, as particular cases, the several classes of summing type multilinear operators that have been studied individually in the literature. Summing operators by blocks in the isotropic and anisotropic cases are taken into account. The classes we create are shown to be Banach ideals of multilinear operators and applications to coherence and coincidence theorems are provided.Geraldo BotelhoDavidson Freitas
Copyright (c) 2024 Geraldo Botelho, Davidson Freitas
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2024-06-162024-06-1661764410.12775/TMNA.2023.033Gromov-Hausdorff stability for semilinear systems with large diffusion
https://apcz.umk.pl/TMNA/article/view/52721
This paper deals with the Gromov-Hausdorff stability for systems generated of reaction-diffusion equations whose diffusion coefficients are simultaneously large in a bounded smooth domains. The appropriated framework is presented to establish the conjugation between the attractors by means o f $\varepsilon$-isometries.Jihoon LeeNgocthach NguyenLeonardo Pires
Copyright (c) 2024 Jihoon Lee, Ngocthach Nguyen, Leonardo Pires
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2024-06-162024-06-1664565910.12775/TMNA.2023.034On the fractional-in-time Keller-Segel model via Sonine kernels
https://apcz.umk.pl/TMNA/article/view/52722
In this paper, we study the existence and asymptotic behavior to a diffusion system which is non-local in time. As consequence of our theorems we deduce new results for the fractional-in-time Keller-Segel model. Our approach is intimately related with the Sonine kernels.Masterson CostaClaudio CuevasClessius SilvaHerme Soto
Copyright (c) 2024 Masterson Costa, Claudio Cuevas, Clessius Silva, Herme Soto
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2024-06-162024-06-1666168510.12775/TMNA.2023.035Optimal control, well-posedness and sensitivity analysis for a class of generalized evolutionary systems
https://apcz.umk.pl/TMNA/article/view/52723
In this paper, we are concerned with a generalized evolution dynamical system, called fractional differential variational-hemivariational inequality (FDVHVI, for short), which is composed of a nonlinear fractional evolution inclusion and a time-dependent mixed variational-hemivariational inequality in the framework of Banach spaces. The objective of this paper is four fold. The first one is to investigate the nonemptiness as well as the compactness of the mild solutions set to the FDVHVI. The second aim is to study the optimal control problems described by the FDVHVI. The third goal is to establish the well-posedness results of the FDVHVI, including the existence, uniqueness, and stability. Furthermore, the sensitivity analysis of a perturbed problem associated to the FDVHVI with respect to the initial state and the two parameters is also obtained. Finally, a comprehensive fractional model is given to illustrate the validity of our main results.Xiuwen LiZhi LuoZhenhai Liu
Copyright (c) 2024 Xiuwen Li, Zhi Luo, Zhenhai Liu
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2024-06-162024-06-1668771610.12775/TMNA.2023.036A multiplicity result for critical elliptic problems involving differences of local and nonlocal operators
https://apcz.umk.pl/TMNA/article/view/52724
We study some critical elliptic problems involving the difference of two nonlocal operators, or the difference of a local operator and a nonlocal operator. The main result is the existence of two nontrivial weak solutions, one with negative energy and the other with positive energy, for all sufficiently small values of a parameter. The proof is based on an abstract result recently obtained in \cite{MR4293883}.Kanishka PereraCaterina Sportelli
Copyright (c) 2024 Kanishka Perera, Caterina Sportelli
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2024-06-162024-06-1671773110.12775/TMNA.2023.037A class of double phase problem without Ambrosetti-Rabinowitz-type growth condition: infinitely many solutions
https://apcz.umk.pl/TMNA/article/view/52725
This paper concerns with a class of double phase problem without Ambrosetti-Rabinowitz-type growth condition. Under reasonable hypotheses, we establish the existence of infinitely many solutions by using the variant fountain theorems due to Zou \cite{71}.Bin GeYuhang HanQinghai CaoHaixin Ren
Copyright (c) 2024 Bin Ge, Yuhang Han, Qinghai Cao, Haixin Ren
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2024-06-162024-06-1673374810.12775/TMNA.2023.040