Positive solutions for nonlinear singular elliptic equations of p-Laplacian type with dependence on the gradient

By Zhenhai Liu, Dumitru Motreanu, Shengda Zeng. Calculus of Variations and Partial Differential Equations, 2019

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In this paper, we study a nonlinear Dirichlet problem of p-Laplacian type with combined effects of nonlinear singular and convection terms. An existence theorem for positive solutions is established as well as the compactness of solution set. Our approach is based on Leray–Schauder alternative principle, method of sub-supersolution, nonlinear regularity, truncation techniques, and set-valued analysis.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/ab3f4e198ac377fe0296b9c87a4442b282c94641