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

Farajollah Mohammadi Yaghoobi, Jamil‎eh ‎Shamshiri


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.‎‎


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

Full Text: PDF


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.