Singular quasilinear elliptic problems with convection terms

TL;DR

This paper reviews recent advances in solving quasilinear elliptic equations with singular and convection terms, focusing on existence, uniqueness, and multiplicity of solutions under various boundary conditions.

Contribution

It introduces new results on solution properties for complex elliptic problems using advanced mathematical techniques and discusses the impact of different boundary conditions.

Findings

Existence of solutions established via sub-supersolution and fixed point methods.

Uniqueness and multiplicity derived from monotonicity arguments.

Boundary conditions significantly influence solution behavior.

Abstract

In this paper we present some very recent results regarding existence, uniqueness, and multiplicity of solutions for quasilinear elliptic equations and systems, exhibiting both singular and convective reaction terms. The importance of boundary conditions (Dirichlet, Neumann, or Robin) is also discussed. Existence is achieved via sub-supersolution and truncation techniques, fixed point theory, nonlinear regularity, and set-valued analysis, while uniqueness and multiplicity are obtained by monotonicity arguments.