APPLICATION OF MOUNTAIN PASS THEOREM TO SUPERLINEAR EQUATIONS WITH FRACTIONAL LAPLACIAN CONTROLLED BY DISTRIBUTED PARAMETERS AND BOUNDARY DATA

In the paper we consider a boundary value problem involving a differential equation with the fractional Laplacian (-Delta)(alpha/2) for alpha is an element of(1, 2) and some superlinear and subcritical nonlinearity G(z) provided with a nonhomogeneous Dirichlet exterior boundary condition. Some sufficient conditions under which the set of weak solutions to the boundary value problem is nonempty and depends continuously in the Painleve-Kuratowski sense on distributed parameters and exterior boundary data are stated. The proofs of the existence results rely on the Mountain Pass Theorem.