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Related papers: Higher nonlocal problems with bounded potential

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In this paper, we consider the dual fractional parabolic problem in the right half space. We prove that the positive solutions are strictly increasing in $x_1$ direction without assuming the solutions be bounded. So far as we know, this is…

Analysis of PDEs · Mathematics 2023-03-21 Wenxiong Chen , Lingwei Ma

In this paper we consider optimal control problems in the nonlocal function space framework of Bellido-2023, where there are two different parameters: a horizon parameter $\delta > 0$; and a fractional parameter $s \in (0, 1)$. The…

Optimization and Control · Mathematics 2026-05-12 Javier Cueto , Joshua M. Siktar

Graph-based analysis holds both theoretical and applied significance, attracting considerable attention from researchers and yielding abundant results in recent years. However, research on fractional problems remains limited, with most of…

Analysis of PDEs · Mathematics 2025-06-10 Mengjie Zhang , Yong Lin , Yunyan Yang

Time fractional parabolic problem for p-Laplacian with double singular Hardy-type potential is considered. Comparison principle and appriory estimates for the weak solutions are proved. Existence of global weak solutions and finite-time…

Analysis of PDEs · Mathematics 2026-03-17 Nikolai Kutev , Tsviatko Rangelov

We study a class of nonlinear non-autonomous nonlocal equations with subcritical and critical exponential nonlinearity. The involved potential can vanish at infinity.

Analysis of PDEs · Mathematics 2014-11-04 João Marcos do Ó , Olimpio H. Miyagaki , Marco Squassina

In this PhD thesis, we deal with problems related to nonlocal operators, in particular to the fractional Laplacian and to some other types of fractional derivatives (the Caputo and the Marchaud derivatives). We make an extensive…

Analysis of PDEs · Mathematics 2017-05-03 Claudia Bucur

The present paper studies the fractional $p$-Laplacian boundary value problems with jumping nonlinearities at zero or infinity and obtain the existence of multiple solutions and sign-changing solutions by constructing the suitable…

Analysis of PDEs · Mathematics 2020-09-09 Debangana Mukherjee

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

Recently, great attention has been focused on the study of fractional and non-local operators of elliptic type, both for pure mathematical research and in view of concrete real-world applications. Our problem is related to the fractional…

Analysis of PDEs · Mathematics 2025-06-25 Sana Benhafsia , Rejeb Hadiji

We present a construction of harmonic functions on bounded domains for the spectral fractional Laplacian operator and we classify them in terms of their divergent profile at the boundary. This is used to establish and solve boundary value…

Analysis of PDEs · Mathematics 2015-09-22 Nicola Abatangelo , Louis Dupaigne

In this paper we investivate bifurcation results for a class of problem in a smooth bounded domain involving the fractional p-Laplacian operator and with a nonlinearity that reaches the critical growth with respect to the fractional Sobolev…

Analysis of PDEs · Mathematics 2015-05-14 Kanishka Perera , Marco Squassina , Yang Yang

This paper is devoted to study a fractional Choquard problem with slightly subcritical exponents on bounded domains. When the exponent of the convolution type nonlinearity tends to the fractional critical one in the sense of…

Analysis of PDEs · Mathematics 2023-02-07 Marco G. Ghimenti , Min Liu , Zhongwei Tang

By exploiting a suitable Trudinger-Moser inequality for fractional Sobolev spaces, we obtain existence and multiplicity of solutions for a class of one-dimensional nonlocal equations with fractional diffusion and nonlinearity at exponential…

Analysis of PDEs · Mathematics 2013-11-12 Antonio Iannizzotto , Marco Squassina

We obtain fundamental imbeddings for the fractional Sobolev space with variable exponent that is a generalization of well-known fractional Sobolev spaces. As an application, we obtain a-priori bounds and multiplicity of solutions to some…

Analysis of PDEs · Mathematics 2018-10-12 Ky Ho , Yun-Ho Kim

We prove the existence of a positive solution for nonlocal problems involving the fractional Laplacian and a critical growth power nonlinearity when the equation is set in a suitable contractible domain.

Analysis of PDEs · Mathematics 2015-04-03 Sunra Mosconi , Naoki Shioji , Marco Squassina

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 consider the divergent fractional Laplace operator presented in [Dipierro-Savin-Valdinoci, Rev. Mat. Iberoam.] and we prove three types of results. Firstly, we show that any given function can be locally shadowed by a solution of a…

Analysis of PDEs · Mathematics 2021-02-04 Serena Dipierro , Ovidiu Savin , Enrico Valdinoci

This work is devoted to study the existence of infinitely many weak solutions to nonlocal equations involving a general integrodifferential operator of fractional type. These equations have a variational structure and we find a sequence of…

Analysis of PDEs · Mathematics 2013-12-16 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

We study elliptic equations of order $2m$ with nonlocal boundary-value conditions in plane angles and in bounded domains, dealing with the case where the support of nonlocal terms intersects the boundary. We establish necessary and…

Analysis of PDEs · Mathematics 2014-04-22 Pavel Gurevich