# Fixed point index theory for decomposable multivalued maps and applications to φ-Laplacian problems

## Abstract

In this paper, we develop a fixed point index theory for decomposable multivalued maps, that is, compositions of two multivalued nonlinear upper semicontinuous maps. As an application, this fixed point index theory is combined with the method of lower and upper solutions in order to obtain new existence, localization and multiplicity results for  $$\phi$$-Laplacian problems with discontinuous nonlinearities and nonlinear functional boundary conditions.

## 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, 15782, Facultade de Matemáticas, Campus Vida, Santiago, Spain

## Keywords

Fixed point index theory; Discontinuous differential equation; Multiple solutions; ϕ-Laplacian equation; Lower and upper solutions

## Paper coordinates

R. Precup, J. Rodríguez-López, Fixed point index theory for decomposable multivalued maps and applications to φ-Laplacian problems, Nonlinear Anal. 199 (2020) 111958, 16 p., http://doi.org/10.1016/j.na.2020.111958

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