On singular $p$-Laplacian problems with discontinuous convection terms

TL;DR

This paper proves the existence of positive solutions for a singular p-Laplacian problem with discontinuous nonlinearities and convection terms, using measure-theoretic locality arguments.

Contribution

It introduces a novel approach employing measure-theoretic locality arguments to handle discontinuities and singularities in p-Laplacian problems.

Findings

Existence of positive strong solutions established.

Handles highly discontinuous nonlinearities.

Employs measure-theoretic locality techniques.

Abstract

The existence of positive strong solutions to a homogeneous Dirichlet $p$-Laplacian problem, with reaction sum of a both singular at zero and highly discontinuous nonlinearity and of a discontinuous convection term, is established. Locality arguments, based on suitable measure theoretical results (see Section 3), are employed.