Variational methods for non-local operatorsof elliptic type

In this paper we study the existence of non-trivial solutions forequations driven by a non-local integrodifferentialoperator $\mathcal L_K$ with homogeneous Dirichlet boundaryconditions. More precisely, we consider the problem$$ \left\{\begin{array}{ll}\mathcal L_K u+\lambda u+f(x,u)=0 in Ω \\u=0 in \mathbb{R}^n \backslash Ω ,\end{array} \right.$$where $\lambda$ is a real parameter and the nonlinear term $f$satisfies superlinear and subcritical growth conditions at zero andat infinity. This equation has a variational nature, and so itssolutions can be found as critical points of the energy functional$\mathcal J_\lambda$ associated to the problem. Here we get suchcritical points using both the Mountain Pass…

• MD
  Ministero dell’Istruzione, dell’Università e della Ricerca