https://apcz.umk.pl/TMNA/issue/feedTopological Methods in Nonlinear Analysis2023-12-31T17:25:05+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 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>https://apcz.umk.pl/TMNA/article/view/46992Multiple cylindrically symmetric solutions of nonlinear Maxwell equations2023-11-19T11:15:18+01:00Yanyun Wenwenyy19@lzu.edu.cnPeihao Zhaozhaoph@lzu.edu.cnIn this paper, we study the following nonlinear time-harmonic Maxwell equations \begin{equation}\label{equation 0.1} \nabla\times(\nabla \times E)-\omega^2\varepsilon(x)E =P(x)|E|^{p-2}E+Q(x)|E|^{q-2}E, \end{equation} where $\varepsilon(x)$ is the permittivity of the material, $x\in\mathbb{R}^{3}$, $1< q< {p}/({p-1})< 2< p< 6$, $P(x),Q(x)\in C\left(\mathbb{R}^{3},\mathbb{R}\right)$. Under some special cylindrical symmetric conditions for $\varepsilon(x)$, $P(x)$ and $Q(x)$, we obtain infinite many cylindrically symmetric solutions of \eqref{equation 0.1} by using variational method and fountain theorems without $\tau$-upper semi-continuity.2023-11-19T00:00:00+01:00Copyright (c) 2023 Yanyun Wen, Peihao Zhaohttps://apcz.umk.pl/TMNA/article/view/47710The existence of multiple topologically distinct solutions to $\sigma_{2,p}$-energy2023-12-31T17:25:04+01:00Mojgan Taghavitmna@ncu.plMohammad S. Shahrokhi-Dehkordim_shahrokhi@sbu.ac.irLet ${\An} \subset \R^n$ be a bounded Lipschitz domain and consider the $\sigmap$-energy functional \begin{equation*} {{\mathbb F}_{\sigmap}}[u; {\An}] := \int_{\An} \big|{\wedge}^2 \nabla u\big|^p dx, \end{equation*} with $p\in\mathopen]1, \infty]$ over the space of measure preserving maps \begin{equation*} {\mathcal A}_p(\An) =\big\{u \in W^{1,2p}\big(\An, \R^n\big) : u|_{\partial \An} = {x},\ \det \nabla u =1 \mbox{ for ${\mathcal L}^n$-a.e.\ in $\An$} \big\}. \end{equation*} In this article we address the question of multiplicity {\it versus} uniqueness for {\it extremals} and {\it strong} local minimizers of the $\sigmap$-energy funcional $\mathbb F_{\sigmap}[\cdot; {\An}]$ in ${\mathcal A}_p({\An})$. We use a topological class of maps referred to as {\it generalised} twists and examine them in connection with the Euler-Lagrange equations associated with $\sigmap$-energy functional over ${\mathcal A}_p({\An})$. Most notably, we prove the existence of a countably infinite of topologically distinct twisting solutions to the later system in all {\it even} dimensions by linking the system to a set of nonlinear isotropic ODEs on the Lie group ${\rm SO}(n)$. In sharp contrast in {\it odd} dimensions the only solution is the map $u\equiv x$. The result relies on a careful analysis of the {\it full} versus the {\it restricted} Euler-Lagrange equations. Indeed, an analysis of curl-free vector fields generated by symmetric matrix fields plays a pivotal role.2023-12-31T00:00:00+01:00Copyright (c) 2023 Mojgan Taghavi, Mohammad S. Shahrokhi-Dehkordihttps://apcz.umk.pl/TMNA/article/view/47707A noniterative reconstruction method for the inverse potential problem for a time-fractional diffusion equation2023-12-31T17:25:04+01:00Mohamed BenSalahmohamed.bensalah@fsm.rnu.tnThis paper is concerned with the reconstruction of the support of the potential term for a time-fractional diffusion equation from the final measured data. The aim of this paper is to propose an accurate approach based on the topological derivative method. The idea is to formulate the reconstruction problem as a topology optimization one minimizing a given cost function. We derive a topological asymptotic expansion for the fractional model. The unknown support is reconstructed using the level-set curve of the topological gradient. We finally make some numerical examples proving the efficiency and accuracy of the proposed algorithm.2023-12-31T00:00:00+01:00Copyright (c) 2023 Mohamed BenSalahhttps://apcz.umk.pl/TMNA/article/view/47711Concentrating solutions for a biharmonic problem with supercritical growth2023-12-31T17:25:04+01:00Zhongyuan Liuliuzy@henu.edu.cnIn this paper we consider the following supercritical biharmonic problem: $$ \begin{cases} \Delta^2 u= K(x)u^{p+\epsilon}&\text{in } \Omega,\\ u> 0 &\text{in }\Omega,\\ u=\Delta u=0&\text{on }\partial\Omega, \end{cases} $$ where $K(x)\in C^3(\overline{\Omega})$ is a nonnegative function, $p=({N+4})/({N-4})$, $\epsilon> 0$, $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$, $N\geq6$. We show that, for $\epsilon$ small enough, there exists a family of concentrating solutions under certain assumptions on the critical points of the function $K(x)$.2023-12-31T00:00:00+01:00Copyright (c) 2023 Zhongyuan Liuhttps://apcz.umk.pl/TMNA/article/view/47717Exponential attractor for the Cahn-Hilliard-Oono equation in R^N2023-12-31T17:25:05+01:00Jan W. Cholewajan.cholewa@us.edu.plRadosław Czajaradoslaw.czaja@us.edu.plWe consider the Cahn-Hilliard-Oono equation in the whole of $\mathbb{R}^N$, $N\leq 3$. We prove the existence of an exponential attractor in $H^1\big(\mathbb{R}^N\big)$, which contains a global attractor. We also estimate from above fractal dimension of the attractors.2023-12-31T00:00:00+01:00Copyright (c) 2023 Jan W. Cholewa, Radosław Czajahttps://apcz.umk.pl/TMNA/article/view/47706Normalized solutions for the Schrödinger-Poisson system with doubly critical growth2023-12-31T17:25:04+01:00Yuxi Mengyxmeng125@163.comXiaoming Hexmhe923@muc.edu.cnIn this paper we are concerned with normalized solutions to the Schrödinger-Poisson system with doubly critical growth \[ \begin{cases} -\Delta u-\phi |u|^3u=\lambda u+\mu|u|^{q-2}u+|u|^4u, &x \in \R^{3},\\ -\Delta \phi=|u|^5, &x \in \R^{3}, \end{cases} \] and prescribed mass \[ \int_{\R^3}|u|^2dx=a^2,\] where $a> 0$ is a constant, $\mu> 0$ is a parameter and $2< q< 6$. In the $L^2$-subcritical case, we study the multiplicity of normalized solutions by applying the truncation technique, and the genus theory; and in the $L^2$-supercritical case, we obtain a couple of normalized solutions by developing a fiber map. Under both cases, to recover the loss of compactness of the energy functional caused by the critical growth, we need to adopt the concentration-compactness principle. Our results complement and improve some related studies for the Schrödinger-Poisson system with nonlocal critical term in the literature.2023-12-31T00:00:00+01:00Copyright (c) 2023 Yuxi Meng, Xiaoming Hehttps://apcz.umk.pl/TMNA/article/view/47712Fixed point theorems in partially ordered topological spaces with applications2023-12-31T17:25:04+01:00Mohamed Aziz Taoudia.taoudi@uca.maIn this paper, we establish several new fixed point results in the framework of topological spaces endowed with a partial order. Special attention is paid to the case that the topology is induced by a metric. Our conclusions generalize many well-known results. Several examples and illustrative applications are provided to support the exposed results.2023-12-31T00:00:00+01:00Copyright (c) 2023 Mohamed Aziz Taoudihttps://apcz.umk.pl/TMNA/article/view/47713Balanced capacities2023-12-31T17:25:05+01:00Taras Radultarasradul@yahoo.co.ukWe consider capacity (fuzzy measure, non-additive probability) on a compactum as a monotone cooperative normed game. Then it is natural to consider probability measures as elements of core of such game. We prove a topological version of the Bondareva-Shapley theorem that non-emptiness of the core is equivalent to balancedness of the capacity. We investigate categorical properties of balanced capacities and give characterizations of some fuzzy integrals of balanced capacities.2023-12-31T00:00:00+01:00Copyright (c) 2023 Taras Radulhttps://apcz.umk.pl/TMNA/article/view/47714On the $S$-asymptotically $\omega$-periodic mild solutions for multi-term time fractional measure differential equations2023-12-31T17:25:05+01:00Haide Gou842204214@qq.comIn this paper, based on regulated functions and fixed point theorem, a class of nonlocal problem of multi-term time-fractional measure differential equations involving nonlocal conditions in Banach spaces. Firstly, we introduce the concept of $S$-asymptotically $\omega$-periodic mild solution, on the premise of by utilizing $(\beta,\gamma_k)$-resolvent family and measure functional (Henstock-Lebesgue-Stieltjes integral), the existence of $S$ -asymptotically $\omega$ periodic mild solutions for the mentioned system are obtained. Finally, as the application of abstract results, the existence $S$-asymptotically $\omega$-periodic mild solution for a classes of measure driven differential equation are discussed.2023-12-31T00:00:00+01:00Copyright (c) 2023 Haide Gouhttps://apcz.umk.pl/TMNA/article/view/46318A note on positive solutions of Lichnerowicz equations involving the $\Delta_\lambda$-Laplacian2023-09-23T22:42:50+02:00Anh Tuan Duongtuan.duonganh@hust.edu.vnThi Quynh Nguyennguyen.quynh@haui.edu.vnIn this paper, we are concerned with the parabolic Lichnerowicz equation involving the $\Delta_\lambda$-Laplacian $$ v_t-\Delta_\lambda v=v^{-p-2}-v^p,\quad v> 0, \quad \mbox{ in }\mathbb R^N\times\mathbb R, $$ where $p> 0$ and $\Delta_\lambda$ is a sub-elliptic operator of the form $$ \Delta_\lambda=\sum_{i=1}^N\partial_{x_i}\big(\lambda_i^2\partial_{x_i}\big). $$ Under some general assumptions of $\lambda_i$ introduced by A.E. Kogoj and E. Lanconelli in Nonlinear Anal. {\bf 75} (2012), no.\ 12, 4637-4649, we shall prove a uniform lower bound of positive solutions of the equation provided that $p> 0$. Moreover, in the case $p> 1$, we shall show that the equation has only the trivial solution $v=1$. As a consequence, when $v$ is independent of the time variable, we obtain the similar results for the elliptic Lichnerowicz equation involving the $\Delta_\lambda$-Laplacian $$ -\Delta_\lambda u=u^{-p-2}-u^p,\quad u> 0,\quad \mbox{in }\mathbb R^N. $$2023-09-23T00:00:00+02:00Copyright (c) 2023 Anh Tuan Duong, Thi Quynh Nguyenhttps://apcz.umk.pl/TMNA/article/view/47715On a class of Hausdorff measure of cartesian product sets in metric spaces2023-12-31T17:25:05+01:00Najmeddine Attianattia@kfu.edu.saHajer Jebalihajer.jebali@fsm.rnu.tnRihab Guedririhabguedri096@gmail.comIn this paper we study, in a separable metric space, a class of Hausdorff measures ${\mathcal H}_\mu^{q, \xi}$ defined using a measure $\mu$ and a premeasure $\xi$. We discuss a Hausdorff structure of product sets. Weighted Hausdorff measures ${\mathcal W}_\mu^{q, \xi}$ appeare as an important tool when studying the product sets. When $\mu$ and $\xi$ satisfy the doubling condition, we prove that ${\mathcal H}_\mu^{q, \xi} = {\mathcal W}_\mu^{q, \xi}$. As an application, the case where $\xi$ is defined as the Hausdorff function is considered.2023-12-31T00:00:00+01:00Copyright (c) 2023 Najmeddine Attia, Hajer Jebali, Rihab Guedrihttps://apcz.umk.pl/TMNA/article/view/47716Periodic solutions with irrational frequency for a class of semilinear wave equations with variable coefficients2023-12-31T17:25:05+01:00Hui Weiweihui01@163.comThis paper is devoted to the study of the existence of periodic solutions for a class of semilinear wave equations with variable coefficients. The forced vibrations of a nonhomogeneous string and propagation of seismic waves in nonisotropic media is governed by this mathematical model. When the frequency is a sufficiently large irrational number with bounded partial quotients, the existence of weak solutions is established. Then, under some suitable conditions, we improve the regularity of weak solutions. Our results can also be applied to the corresponding constant coefficients wave equation.2023-12-31T00:00:00+01:00Copyright (c) 2023 Hui Weihttps://apcz.umk.pl/TMNA/article/view/47718A direct proof of existence of weak solutions to elliptic problems2023-12-31T17:25:05+01:00Iwona Chlebickai.chlebicka@mimuw.edu.plArttu Karppinena.karppinen@uw.edu.plYing Lilyinsh@shu.edu.cnWe provide a direct proof of existence and uniqueness of weak solutions to a broad family of strongly nonlinear elliptic equations with lower-order terms. The leading part of the operator satisfies general growth conditions settling the problem in the framework of fully anisotropic and inhomogeneous Musielak-Orlicz spaces generated by an $N$-function \linebreak $M\colon \Omega\times\mathbb R^d\to [0,\infty)$. Neither $\nabla_2$ nor $\Delta_2$ conditions are imposed on $M$. Our results cover among others problems with anisotropic polynomial, Orlicz, variable exponent, and double phase growth.2023-12-31T00:00:00+01:00Copyright (c) 2023 Iwona Chlebicka, Arttu Karppinen, Ying Lihttps://apcz.umk.pl/TMNA/article/view/47708Existence and multiplicity of radially symmetric solutions for nonlinear Schrödinger equations2023-12-31T17:25:04+01:00Tomoharu Kinoshitaluzhiqing@akane.waseda.jpIn this paper we study the following nonlinear Schrödinger equations in $\mathbb{R}^N$: $$ -\Delta u + V(x)u= g(u),\quad u \in H^1(\mathbb{R}^N), $$ where $N \ge 2$, $V \in C^1(\mathbb{R}^N,\mathbb{R})$ and $g \in C(\mathbb{R},\mathbb{R}).$ For a wide class of nonlinearities, which satisfy the Berestycki-Lions type condition, we show the existence and multiplicity of radially symmetric solutions. We use a new deformation argument under a new version of the Palais-Smale condition.2023-12-31T00:00:00+01:00Copyright (c) 2023 Tomoharu Kinoshitahttps://apcz.umk.pl/TMNA/article/view/47719Multiple mixed interior and boundary peaks synchronized solutions for linearly coupled Schrödinger systems2023-12-31T17:25:05+01:00Ke JinKJin16@zjnu.edu.cnIn the present paper we consider the problem: \begin{equation} \label{0}\tag{N$_\varepsilon$} \begin{cases} -\varepsilon^{2}\Delta u+u=u^{3}+\lambda v& \text{in } \Omega, \\ -\varepsilon^{2}\Delta v+v=v^{3}+\lambda u& \text{in } \Omega,\\ u> 0,\ v> 0& \text{in } \Omega,\\ \dfrac{\partial u}{\partial n}=\dfrac{\partial v}{\partial n}=0& \text{on } \partial\Omega, \end{cases} \end{equation} where $\varepsilon> 0$, $0< \lambda< 1$, $\Omega\subset\mathbb{R}^{3}$ is smooth and bounded, and $n$ denotes the outer normal vector defined on $\partial\Omega$, the boundary of $\Omega$. By the Lyapunov-Schmidt reduction method and the maximum principle of elliptic equations, we construct synchronized solutions of (\ref{0}) with mixed interior and boundary peaks for any $0< \varepsilon< \varepsilon_0$ and $\lambda\in(0,1)\backslash\{\lambda_0\}$, where $\lambda_0\in(0,1)$ is given and $\varepsilon_0> 0$ is sufficiently small. As $\varepsilon$ approaches $0$, the interior peaks concentrate at sphere packing points in $\Omega$ and the boundary peaks concentrate at the critical points of the mean curvature function of the boundary.2023-12-31T00:00:00+01:00Copyright (c) 2023 Ke Jinhttps://apcz.umk.pl/TMNA/article/view/47720Multiple solutions of nonlinear Neumann inclusions2023-12-31T17:25:05+01:00Filomena Cianciarusofilomena.cianciaruso@unical.itPaolamaria Pietramalapietramala@unical.itWe prove new results on the existence of multiple solutions for elliptic inclusions with nonlinear boundary conditions of Neumann type. Our approach is topological and relies on the fixed point index for multivalued map.2023-12-31T00:00:00+01:00Copyright (c) 2023 Filomena Cianciaruso, Paolamaria Pietramala