Positive Solutions for Nonlinear Dirichlet Problems with Convection

Abstract

We consider a nonlinear Dirichlet problem driven by the p-Laplacian, a convection term and a (p- 1 ) -sublinear perturbation. First we assume that the coefficient in the convection term (drift coefficient) is sign changing. Using the theory of nonlinear operators of monotone type together with suitable truncation and comparison techniques we prove the existence of a positive smooth solution. When the drift coefficient is nonnegative, we are able to relax the conditions on the data of the problem.

Document Type

Article

DOI

https://doi.org/10.1007/s00245-018-9534-5

Keywords

Convection term, Indefinite drift coefficient, Nonlinear Krein–Rutman theorem, Nonlinear maximum principle, Nonlinear regularity, Truncation

Publication Date

1-1-2018

Journal Title

Applied Mathematics and Optimization

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