Existence of Three Nontrivial Smooth Solutions for Nonlinear Resonant Neumann Problems Driven by the $p$-Laplacian | Zendy

Leszek Gasiński | Zendy; Nikolaos S. Papageorgiou | Zendy

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Existence of Three Nontrivial Smooth Solutions for Nonlinear Resonant Neumann Problems Driven by the $p$-Laplacian

Author(s) -

Leszek Gasiński,

Nikolaos S. Papageorgiou

Publication year - 2010

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1415

Subject(s) - nonlinear system , laplace operator , von neumann architecture , p laplacian , mathematics , neumann boundary condition , mathematical analysis , pure mathematics , mathematical physics , physics , boundary value problem , quantum mechanics

We consider a nonlinear Neumann elliptic problem driven by the p-Laplacian and with a reaction term which asymptotically at ±∞ exhibits resonance with respect to the principal eigenvalue λ0 = 0. Using variational methods combined with tools from Morse theory, we show that the resonant problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive, the other negative). © European Mathematical Society

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