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 6, 2019.
Math Subject Classifications: 35J91, 47B25, 47F05.
Key Words: Phrase Fractional Dirichlet-Laplace operator; Stone-von Neumann operator calculus' variational methods.
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| Dariusz Idczak |
Faculty of Mathematics and Computer Science
University of Lodz
90-238 Lodz, Banacha 22 Poland
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