Existence of solution for a class ‎of‎ fractional ‎problems with sign-changing ‎functions

Authors

  • Farajollah Mohammadi Yaghoobi Hamedan Branch‎, ‎Islamic Azad University‎‎‎
  • Jamil‎eh ‎Shamshiri Tabaran Institute of Higher ‎Education‎‎

DOI:

https://doi.org/10.30495/jme.v15i0.2008

Keywords:

Critical ‎points‎, ‎ ‎Fractional partial differential ‎equations, ‎W‎eak ‎solutions, ‎ ‎Nehari ‎manifold, ‎F‎ibering map.‎‎‎‎

Abstract

Here we study the existence and multiplicity of solutions for the ‎following‎ ‎fractional‎‎ problem‎

‎$$‎ ‎(-\Delta)_p^s u+a(x) |u|^‎{‎‎p‎-2} ‎u‎= f(x,u)‎, ‎$$‎

‎with ‎the ‎Dirichlet‎ boundary condition $u=0$ on $\partial\Omega$‎

‎where $\Omega$ is a bounded domain with smooth boundary‎, ‎$p\geq 2$‎,‎ $s\in(0,1)$ and ‎‎$‎a(x)‎‎$‎ ‎is a‎ sign-changing ‎function.‎

‎Moreover, we consider two different assumptions on the ‎function‎ $‎f(x,u)‎$‎,

‎including the cases of nonnegative and sign-changing ‎function.‎‎

Author Biographies

Farajollah Mohammadi Yaghoobi, Hamedan Branch‎, ‎Islamic Azad University‎‎‎

Department of Mathematics‎,

Hamedan‎ Branch‎, ‎Islamic Azad ‎University,

Hamedan‎, ‎Iran‎

Jamil‎eh ‎Shamshiri, Tabaran Institute of Higher ‎Education‎‎

Department ‎of ‎Accounting‎‎, Mashhad

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Published

2021-07-04

Issue

Section

Vol. 15, No. 5, (2021)