Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 59, pp. 1-17.

Title: Bipolynomial fractional Dirichlet-Laplace problem

Author: Dariusz Idczak (Univ. of Lodz, Banacha 22, Poland)

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.

Submitted July 24, 2018. Published May 06, 2019.
Math Subject Classifications: 35J91, 47B25, 47F05.
Key Words: Phrase Fractional Dirichlet-Laplace operator;
           Stone-von Neumann operator calculus' variational methods.