# Positive solutions for discontinuous problems with applications to ϕ-Laplacian equations

## Abstract

We establish existence and localization of positive solutions for general discontinuous problems for which a Harnack-type inequality holds. In this way, a wide range of ordinary differential problems such as higher order boundary value problems or $$\phi$$-Laplacian equations can be treated. In particular, we study the Dirichlet–Neumann problem involving the $$\phi$$-Laplacian. Our results rely on Bohnenblust–Karlin fixed point theorem which is applied to a multivalued operator defined in a product space.

## Authors

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

Jorge Rodríguez-López
Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas,
Universidade de Santiago de Compostela, Facultade de Matemáticas, Campus Vida, 15782, Santiago, Spain

## Keywords

Discontinuous differential equations; positive solution; multiple solutions; $$\phi$$-Laplacian equations; Bohnenblust–Karlin fixed point theorem.

## Paper coordinates

R. Precup, J. Rodríguez-López, Positive solutions for discontinuous problems with applications to $$\phi$$-Laplacian equations, Journal of Fixed Point Theory and Applications, vol. 20  (2018) art. no. 156, https://doi.org/10.1007/s11784-018-0636-0

## PDF

##### Journal

Journal of Fixed Point Theory and Applications

Springer

16617746

16617738