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In this paper we investigate the existence of multiple solutions for the following two fractional problems \begin{equation*} \left\{\begin{array}{ll} (-\Delta_{\Omega})^{s} u-\lambda u= f(x, u) &\mbox{in} \Omega \\ u=0 &\mbox{in} \partial…

Analysis of PDEs · Mathematics 2018-09-06 Vincenzo Ambrosio

We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators…

Analysis of PDEs · Mathematics 2026-03-12 Serena Dipierro , Edoardo Proietti Lippi , Caterina Sportelli , Enrico Valdinoci

We study the existence and multiplicity of periodic weak solutions for a non-local equation involving an odd subcritical nonlinearity which is asymptotically linear at infinity. We investigate such problem by applying the the pseudo-index…

Analysis of PDEs · Mathematics 2018-09-06 Vincenzo Ambrosio , Giovanni Molica Bisci

The thesis studies linear and semilinear Dirichlet problems driven by different fractional Laplacians. The boundary data can be smooth functions or also Radon measures. The goal is to classify the solutions which have a singularity on the…

Analysis of PDEs · Mathematics 2015-11-03 Nicola Abatangelo

In this paper we establish, using variational methods combined with the Moser-Trudinger inequality, existence and multiplicity of weak solutions for a class of critical fractional elliptic equations with exponential growth without a…

Analysis of PDEs · Mathematics 2020-04-07 Hamilton Bueno , Eduardo Huerto Caqui , Olimpio Miyagaki

It is established the existence and multiplicity of weak solutions for a class of nonlocal equations involving the fractional laplacian, nonlinearities with critical exponential growth and potentials this is which may change sign. The…

Analysis of PDEs · Mathematics 2014-11-19 Manassés de Souza , Yane Lisley Araújo

We deal with a Dirichlet problem driven by the degenerate fractional p-Laplacian and involving a nonlinear reaction which satisfies, among other hypotheses, a (p-1)-linear growth at infinity with non-resonance above the first eigenvalue.…

Analysis of PDEs · Mathematics 2021-10-20 Silvia Frassu , Antonio Iannizzotto

In this paper we study a rather wide class of quasilinear parabolic problems with nonlinear boundary condition and nonstandard growth terms. It includes the important case of equations with a $p(t,x)$-Laplacian. By means of the localization…

Analysis of PDEs · Mathematics 2015-12-15 Patrick Winkert , Rico Zacher

We demonstrate the global existence of weak solutions to a class of semilinear strongly damped wave equations possessing nonlinear hyperbolic dynamic boundary conditions. Our work assumes $(-\Delta_W)^\theta \partial_tu$ with…

Analysis of PDEs · Mathematics 2018-12-27 Joseph L. Shomberg

In this paper, a class of nonlocal fractional Dirichlet problems is studied. By using a variational principle due to Ricceri (whose original version was given in J. Comput. Appl. Math. 113 (2000), 401-410), the existence of infinitely many…

Analysis of PDEs · Mathematics 2023-05-17 Boštjan Gabrovšek , Giovanni Molica Bisci , Dušan D. Repovš

This paper is devoted to the following class of nonlinear fractional Schr\"odinger equations: \begin{equation*} (-\Delta)^{s} u + V(x)u = f(x,u) + \lambda g(x,u), \quad \text{in}\: \mathbb{R}^N, \end{equation*} where $s\in (0,1)$, $N>2s$,…

Analysis of PDEs · Mathematics 2023-01-10 Sofiane Khoutir

We investigate a class of quasi-linear nonlocal problems, including as a particular case semi-linear problems involving the fractional Laplacian and arising in the framework of continuum mechanics, phase transition phenomena, population…

Analysis of PDEs · Mathematics 2014-03-24 Antonio Iannizzotto , Shibo Liu , Kanishka Perera , Marco Squassina

By means of variational methods we investigate existence, non-existence as well as regularity of weak solutions for a system of nonlocal equations involving the fractional laplacian operator and with nonlinearity reaching the critical…

Analysis of PDEs · Mathematics 2015-08-24 Luiz Faria , Olimpio Miyagaki , Fabio Pereira , Marco Squassina , Chengxiang Zhang

This paper presents some sufficient conditions for the existence of solutions of fractional differential equation with nonlocal multi-point boundary conditions involving Caputo fractional derivative and integral boundary conditions. Our…

Classical Analysis and ODEs · Mathematics 2018-11-28 Faouzi Haddouchi

In this paper we consider the existence and multiplicity of weak solutions for the following class of fractional elliptic problem \begin{equation}\label{00} \left\{\begin{aligned} (-\Delta)^{\frac{1}{2}}u + u &= Q(x)f(u)\;\;\mbox{in}\;\;\R…

Analysis of PDEs · Mathematics 2019-10-08 Claudianor O. Alves , César E. Torres Ledesma

We study a Dirichlet-type boundary value problem for a pseudodifferential equation driven by the fractional Laplacian, proving the existence of three nonzero solutions. When the reaction term is sublinear at infinity, we apply the second…

Analysis of PDEs · Mathematics 2016-04-19 Fatma Gamze Düzgün , Antonio Iannizzotto

The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue…

Analysis of PDEs · Mathematics 2016-04-04 Said El Manouni , Hichem Hajaiej , Patrick Winkert

In this work, we study the existence, non-existence, and uniqueness results for nonlocal elliptic equations involving logarithmic Laplacian, and subcritical, critical, and supercritical logarithmic nonlinearities. The Poho\u zaev's identity…

Analysis of PDEs · Mathematics 2025-04-29 Rakesh Arora , Jacques Giacomoni , Arshi Vaishnavi

The aim of this paper is investigating the existence and multiplicity of weak solutions to non--local equations involving the {\em magnetic fractional Laplacian}, when the nonlinearity is subcritical and asymptotically linear at infinity.…

Analysis of PDEs · Mathematics 2023-12-08 Rossella Bartolo , Pietro d'Avenia , Giovanni Molica Bisci

In this paper, we investigate the existence of weak solution for a fractional type problems driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions. We first extend…

Analysis of PDEs · Mathematics 2020-04-03 Elhoussine Azroul , Abdelmoujib Benkirane , Mohammed Srati