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


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.


Radu Precup
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


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

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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


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