English
Related papers

Related papers: Nontrivial solutions of superlinear nonlocal probl…

200 papers

In this paper, we study the solvability of a Cauchy- Dirichlet problem for nonlinear parabolic equation with non standard growths and nonlocal terms. We show the existence of weak solutions of the considered problem under more general…

Analysis of PDEs · Mathematics 2018-03-01 Ugur Sert , Eylem Ozturk

We study a nonlinear, nonlocal Dirichlet problem driven by the fractional p-Laplacian, involving a (p-1)-sublinear reaction. By means of a weak comparison principle we prove uniqueness of the solution. Also, comparing the problem to…

Analysis of PDEs · Mathematics 2023-12-08 Antonio Iannizzotto , Dimitri Mugnai

The purpose of this paper is to investigate the existence of three different weak solutions to a nonlinear elliptic problem that is governed by the weighted {\varphi}-Laplacian operator and subjected to Dirichlet boundary conditions. We…

Analysis of PDEs · Mathematics 2023-09-12 Abderrahmane Lakhdari , Nedra Belhaj Rhouma

In this paper, we are interested in studying the multiplicity, uniqueness, and nonexistence of solutions for a class of singular elliptic eigenvalue problem for the Dirichlet fractional $(p,q)$-Laplacian. The nonlinearity considered…

Analysis of PDEs · Mathematics 2023-06-26 A. L. A. de Araujo , Aldo H. S. Medeiros

We analyze a nonlocal diffusion operator having as special cases the fractional Laplacian and fractional differential operators that arise in several applications. In our analysis, a nonlocal vector calculus is exploited to define a weak…

Analysis of PDEs · Mathematics 2013-03-28 Marta D'Elia , Max Gunzburger

We study the existence and uniqueness of mild and strong solutions of nonlocal nonlinear diffusion problems of $p$-Laplacian type with nonlinear boundary conditions posed in metric random walk spaces. These spaces include, among others,…

Analysis of PDEs · Mathematics 2024-05-24 Marcos Solera , Julián Toledo

We study an elliptic equation, with homogeneous Dirichlet boundary conditions, driven by a mixed type operator (the sum of the Laplacian and the fractional Laplacian), involving a parametric reaction and an undetermined source term.…

Analysis of PDEs · Mathematics 2025-12-02 Antonio Iannizzotto

In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang and the…

Analysis of PDEs · Mathematics 2014-11-04 Sylwia Barnaś

This paper deals with some classes of Kirchhoff type problems on a double phase setting and with nonlinear boundary conditions. Under general assumptions, we provide multiplicity results for such problems in the case when the perturbations…

Analysis of PDEs · Mathematics 2021-12-16 Alessio Fiscella , Greta Marino , Andrea Pinamonti , Simone Verzellesi

In this paper we prove the existence of a weak solution to a doubly nonlinear parabolic fractional $p$-Laplacian equation, which has general doubly non-linearlity including not only the Sobolev subcritical/critical/supercritical cases but…

Analysis of PDEs · Mathematics 2023-05-02 Nobuyuki Kato , Masashi Misawa , Kenta Nakamura , Yoshihiko Yamaura

In this paper, we study a class of quasilinear elliptic equations involving both local and nonlocal operators with variable exponents. The problem exhibits singular nonlinearities along with a subcritical superlinear growth term and a…

Analysis of PDEs · Mathematics 2026-04-08 Shammi Malhotra , Ambesh Kumar Pandey , K. Sreenadh

We establish Ambrosetti -Prodi type results for periodic solutions of one -dimensional nonlinear problems with drift term and drift -less whose principal operator is the fractional Laplacian of order $s\in(0,1)$. We establish conditions for…

Analysis of PDEs · Mathematics 2022-06-27 Begoña Barrios , Lisbeth Carrero , Alexander Quaas

This paper addresses a class of elliptic problems involving the superposition of nonlinear fractional operators with the critical Sobolev exponent in the sublinear regimes. We establish the existence of infinitely many nontrivial weak…

Analysis of PDEs · Mathematics 2026-02-17 Souvik Bhowmick , Sekhar Ghosh , Vishvesh Kumar

This article is a comparative study on an initial-boundary value problem for a class of semilinear pseudo-parabolic equations with the fractional Caputo derivative, also called the fractional Sobolev-Galpern type equations. The purpose of…

Analysis of PDEs · Mathematics 2021-08-18 Huy Tuan Nguyen , Nguyen Anh Tuan , Chao Yang

We consider nonlinear problems governed by the fractional $p-$Laplacian in presence of nonlocal Neumann boundary conditions. We face two problems. First: the $p-$superlinear term may not satisfy the Ambrosetti-Rabinowitz condition. Second,…

Analysis of PDEs · Mathematics 2020-02-12 Dimitri Mugnai , Edoardo Proietti Lippi

We develop some properties of the $p-$Neumann derivative for the fractional $p-$Laplacian in bounded domains with general $p>1$. In particular, we prove the existence of a diverging sequence of eigenvalues and we introduce the evolution…

Analysis of PDEs · Mathematics 2019-04-24 Dimitri Mugnai , Edoardo Proietti Lippi

We establish existence results for a class of mixed anisotropic and nonlocal $p$-Laplace equation with singular nonlinearities. We consider both constant and variable singular exponents. Our argument is based on an approximation method. To…

Analysis of PDEs · Mathematics 2023-03-28 Prashanta Garain , Wontae Kim , Juha Kinnunen

We present explicit formulas for solutions to nonhomogeneous boundary value problems involving any positive power of the Laplacian in the half-space. For non-integer powers the operator becomes nonlocal and this requires a suitable…

Analysis of PDEs · Mathematics 2018-08-14 Nicola Abatangelo , Serena Dipierro , Mouhamed Moustapha Fall , Sven Jarohs , Alberto Saldaña

In this paper, we study the existence of positive non-decreasing radial solutions of a nonlocal non-standard growth problem ruled by the fractional $g$-Laplace operator with exterior Neumann condition. Our argument exploits some properties…

Analysis of PDEs · Mathematics 2024-07-24 Remi Yvant Temgoua

We use a variant of the fountain Theorem to prove the existence of infinitely many weak solutions for the following fractional p-Laplace equation (-\Delta)^{s}_{p}u+V(x)|u|^{p-2}u=f(x,u) in R^N, where $s \in (0,1)$,$ p \geq 2$,$ N \geq 2$,…

Analysis of PDEs · Mathematics 2017-03-07 Vincenzo Ambrosio