On the continuous dependence of solutions to a bipolynomial fractional Dirichlet-Laplace problem

Abstract

In the paper, we consider a bipolynomial fractional Dirichlet-Laplace problem with a functional parameter u. The main goal is to prove theorems on the existence and continuous dependence of solution on functional parameter u for the above problem. Since the solution to the above fractional problem is not unique in general, we use some set-valued approach. We consider two cases (depending on a real parameter a). In the rst case we use a variational method, in the second we apply some abstract results. The obtained results are applied then to a Lagrange problem.

Key words: Fractional Dirichlet-Laplace problem, continuous dependence, variational methods.