Existence of solution for a class of fractional problems with sign-changing functions
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.
Keywords
Critical points, Fractional partial differential equations, Weak solutions, Nehari manifold, Fibering map.
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