| Summary: | In this note, we deal with the existence of infinitely many solutions for a problem driven by nonlocal integro-differential operators with homogeneous Dirichlet boundary conditions
\begin{equation*}
\begin{cases}
-\mathcal{L}_{K}u=\lambda f(x,u), & {\rm in}\ \Omega, \\
u=0, &{\rm in}\;\mathbb{R}^{n}\backslash\Omega, \\
\end{cases}
\end{equation*}
where $\Omega$ is a smooth bounded domain of $\mathbb{R}^{n}$ and the nonlinear term $f$ satisfies superlinear at infinity but does not satisfy the the Ambrosetti–Rabinowitz type condition. The aim is to determine the precise positive interval of $\lambda$ for which the problem admits at least two nontrivial solutions by using abstract critical point results for an energy functional satisfying the Cerami condition.
|
|---|