Existence of solutions for nonlinear equations with mixed local and nonlocal operators

We study an elliptic equation, with homogeneous Dirichlet bound- ary conditions, driven by a mixed type operator (the sum of the Lapla- cian and the fractional Laplacian), involving a parametric reaction and an undetermined source term. Applying a recent abstract critical point theorem of Ricceri, we prove existence of a solution for a convenient source and small enough parameters.