Elliptic Neumann problems with highly discontinuous nonlinearities

This paper investigates nonlinear differential problems involving the p-Laplace operator and subject to Neumann boundary value conditions whereby the right-hand side consists of a nonlinearity which is highly discontinuous. Using variational methods suitable for nonsmooth functionals, we prove the e...

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Bibliographic Details
Published inApplied mathematics letters Vol. 163; p. 109455
Main Authors D’Aguì, Giuseppina, Morabito, Valeria, Winkert, Patrick
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2025
Subjects
Discontinuous nonlinearity
Multiple solution
Neumann problem
Nonsmooth analysis
Multiple solution
Neumann problem
34B15
Discontinuous nonlinearity
Nonsmooth analysis
34A36
49J52
35B30
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Summary:This paper investigates nonlinear differential problems involving the p-Laplace operator and subject to Neumann boundary value conditions whereby the right-hand side consists of a nonlinearity which is highly discontinuous. Using variational methods suitable for nonsmooth functionals, we prove the existence of at least two nontrivial weak solutions of such problems.
ISSN:0893-9659
DOI:10.1016/j.aml.2025.109455