# Positive radial solutions for Dirichlet problems via a Harnack-type inequality

## Abstract

We deal with the existence and localization of positive radial solutions for Dirichlet problems involving $$\phi$$-Laplacian operators in a ball. In particular, $$p$$-Laplacian and Minkowski-curvature equations are considered.

Our approach relies on fixed point index techniques, which work thanks to a Harnack-type inequality in terms of a seminorm. As a consequence of the localization result, it is also derived the existence of several (even infinitely many) positive solutions.

## Authors

Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

Jorge Rodríguez-López
CITMAga and Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago, Spain

## Keywords

compression–expansion, Dirichlet problem, fixed point index, Harnack-type inequality, mean cur-vature operator, Positive radial solution

## Paper coordinates

R. Precup, J. Rodríguez-López, Positive radial solutions for Dirichlet problems via a Harnack-type inequality, Mathematical Methods in the Applied Sciences, 2022, 1-14, https://doi.org/10.1002/mma.8682

## PDF

##### Journal

Mathematical Methods in the Applied Sciences

Wiley

0170-4214

1099-1476