Idczak, Dariusz2021-11-052021-11-052019-05-06Idczak, D. (2019). Bipolynomial fractional Dirichlet-Laplace problem. <i>Electronic Journal of Differential Equations, 2019</i>(59), pp. 1-17.1072-6691https://hdl.handle.net/10877/14792In 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.Text17 pages1 file (.pdf)enAttribution 4.0 InternationalPhrase Fractional Dirichlet-Laplace operatorStone-von Neumann operator calculus' variational methodsArticle