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

  1. Radu Precup 1
  2. Jorge Rodríguez-López 2
  1. 1 Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
  2. 2 Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782, Facultade de Matemáticas, Campus Vida, Santiago, Spain
Journal:
Nonlinear Analysis

ISSN: 0362-546X

Year of publication: 2020

Volume: 199

Pages: 111958

Type: Article

DOI: 10.1016/J.NA.2020.111958 GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Nonlinear Analysis

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 -Laplacian problems with discontinuous nonlinearities and nonlinear functional boundary conditions.