Existence and location of nodal solutions for quasilinear convection-absorption Neumann problems

TL;DR

This paper establishes the existence and precise location of sign-changing and constant sign solutions for quasilinear elliptic equations with convection-absorption terms, using sub-supersolutions and monotone operator methods.

Contribution

It introduces a location principle for nodal solutions and proves the existence of constant sign solutions in the context of convection-absorption quasilinear elliptic problems.

Findings

Existence of nodal solutions is proven.

A location principle for nodal solutions is established.

Constant sign solutions are also shown to exist.

Abstract

Existence of nodal (i.e., sign changing) solutions and constant sign solutions for quasilinear elliptic equations involving convection-absorption terms are presented. A location principle for nodal solutions is obtained by means of constant sign solutions whose existence is also derived. The proof is chiefly based on sub-supersolutions technique together with monotone operator theory.