Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems

Sabri Bahrouni; Hichem Ounaies

doi:10.3934/dcds.2020155

Article Contents

2020, Volume 40, Issue 5: 2917-2944. Doi: 10.3934/dcds.2020155

This issue Previous Article Statistical stability for Barge-Martin attractors derived from tent maps Next Article Pointwise properties of

$ L^p $

-viscosity solutions of uniformly elliptic equations with quadratically growing gradient terms

Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems

Sabri Bahrouni and
Hichem Ounaies

Mathematics Department, Faculty of Sciences, University of Monastir, 5019 Monastir, Tunisia

Received: July 31, 2019

Published: March 2020

The first and second authors are supported by LR 18 ES 15

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Abstract

In the present paper, we deal with a new continuous and compact embedding theorems for the fractional Orlicz-Sobolev spaces, also, we study the existence of infinitely many nontrivial solutions for a class of non-local fractional Orlicz-Sobolev Schrödinger equations whose simplest prototype is

$ (-\triangle)^{s}_{m}u+V(x)m(u) = f(x,u),\ x\in\mathbb{R}^{d}, $

where $ 0<s<1 $, $ d\geq2 $ and $ (-\triangle)^{s}_{m} $ is the fractional $ M $-Laplace operator. The proof is based on the variant Fountain theorem established by Zou.

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Mathematics Subject Classification: Primary: 35J60; Secondary: 35J91, 35S30, 46E35, 58E30.

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