Two Positive Solutions for Elliptic Differential Inclusions

The existence of two positive solutions for an elliptic differential inclusion is established, assuming that the nonlinear term is an upper semicontinuous set-valued mapping with compact convex values having subcritical growth. Our approach is based on variational methods for locally Lipschitz funct...

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Bibliographic Details
Published inAppliedMath Vol. 4; no. 4; pp. 1404 - 1417
Main Authors Bonanno, Gabriele, Morabito, Valeria, O’Regan, Donal, Vassallo, Bruno
Format Journal Article
LanguageEnglish
Published MDPI AG 01.12.2024
Subjects
critical point theory
differential inclusion
second-order elliptic equation
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ISSN2673-9909
2673-9909
DOI10.3390/appliedmath4040074

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Summary:The existence of two positive solutions for an elliptic differential inclusion is established, assuming that the nonlinear term is an upper semicontinuous set-valued mapping with compact convex values having subcritical growth. Our approach is based on variational methods for locally Lipschitz functionals. As a consequence, a multiplicity result for elliptic Dirichlet problems having discontinuous nonlinearities is pointed out.
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath4040074