Abstract
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.
Highlights
Let ⊂ RN (N ≥ 3) be a bounded domain with C2 boundary
We investigate the following singular elliptic equation with Dirichlet boundary condition, p-Laplace differential operator, and a nonlinear convection term:
If p = 2, problem (1) reduces to the semilinear Dirichlet elliptic equation with a singular term and gradient dependence considered by Faraci and Puglisi [14]: ⎧ ⎨ − u(x) = f (x, u(x), ∇u(x)) + g(x, u(x)) in
Summary
We investigate the following singular elliptic equation with Dirichlet boundary condition, p-Laplace differential operator, and a nonlinear convection term (i.e., the reaction function depends on the solution u and its gradient ∇u):. Motreanu received Visiting Professor fellowship from CNPQ/Brazil PV- 400633/2017-5
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