Two Positive Solutions for Elliptic Differential Inclusions

Gabriele Bonanno; Valeria Morabito; Donal O’Regan; Bruno Vassallo

doi:10.3390/appliedmath4040074

Two Positive Solutions for Elliptic Differential Inclusions

Gabriele Bonanno
, Valeria Morabito
, Donal O’Regan
, Bruno Vassallo

Mathematics

Dipartimento DIMED

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1404-1417
Number of pages	14
Journal	AppliedMath
Volume	4
Issue number	4
DOIs	https://doi.org/10.3390/appliedmath4040074
Publication status	Published - Dec 2024

Keywords

critical point theory
differential inclusion
second-order elliptic equation

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10.3390/appliedmath4040074

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title = "Two Positive Solutions for Elliptic Differential Inclusions",

abstract = "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.",

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AU - Bonanno, Gabriele

AU - Morabito, Valeria

AU - O’Regan, Donal

AU - Vassallo, Bruno

PY - 2024/12

Y1 - 2024/12

N2 - 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.

AB - 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.

KW - critical point theory

KW - differential inclusion

KW - second-order elliptic equation

UR - https://www.scopus.com/pages/publications/85213427959

U2 - 10.3390/appliedmath4040074

DO - 10.3390/appliedmath4040074

M3 - Article

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VL - 4

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JO - AppliedMath

JF - AppliedMath

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ER -

Two Positive Solutions for Elliptic Differential Inclusions

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Keywords

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