Bipolynomial fractional Dirichlet-Laplace problem

Abstract

In the article, we derive the existence of solutions for a nonlinear non-autonomous partial elliptic system on an open bounded domain with Dirichlet boundary conditions. This problem contains fractional powers of the weak Dirichlet-Laplace operator in the Stone-von Neumann operator calculus sense. We apply a direct variational method and some results based on the dual least action principle. Both methods give strong solutions of the problem under consideration.