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

Radu Precup; Jorge Rodríguez-López

doi:10.1016/J.NA.2020.111958

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

Radu Precup ¹
Jorge Rodríguez-López ²

1 Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
2 Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782, Facultade de Matemáticas, Campus Vida, Santiago, Spain

Revista:

Nonlinear Analysis

ISSN: 0362-546X

Ano de publicación: 2020

Volume: 199

Páxinas: 111958

Tipo: Artigo

DOI: 10.1016/J.NA.2020.111958 GOOGLE SCHOLAR Acceso aberto editor

Outras publicacións en: Nonlinear Analysis

Resumo

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.