Nonstandard Dirichlet problems with competing (p, q)-Laplacian, convection, and convolution - MOTREANU, Dumitru; MOTREANU, Viorica Venera (Studia Universitatis Babeș-Bolyai Mathematica, 2021)
The paper focuses on a nonstandard Dirichlet problem driven by the operator −∆p +µ∆q , which is a competing (p, q)-Laplacian with lack of ellipticity if µ > 0, and exhibiting a reaction term in the form of a convection (i.e., it depends on the solution and its gradient) composed with the convolution of the solution with an integrable function. We prove the existence of a generalized solution through a combination of fixed-point approach and approximation. In the case µ ≤ 0, we obtain the existence of a weak solution to the respective elliptic problem. Mathematics Subject Classification (2010): 35J92, 47H30.