Osaka Journal of Mathematics

Multiple solutions for superlinear $p$-Laplacian Neumann problems

Abstract

Our main goal is to prove the existence of multiple solutions with precise sign information for a Neumann problem driven by the $p$-Laplacian differential operator with a ($p-1$)-superlinear term which does not satisfy the Ambrosetti--Rabinowitz condition. Using minimax methods we show that the problem has five nontrivial smooth solutions, two positive, two negative and the fifth nodal. In the semilinear case ($p = 2$), using Morse theory, we produce a second nodal solution (for a total of six nontrivial smooth solutions).

Article information

Source
Osaka J. Math., Volume 49, Number 3 (2012), 699-740.

Dates
First available in Project Euclid: 15 October 2012

https://projecteuclid.org/euclid.ojm/1350306594

Mathematical Reviews number (MathSciNet)
MR2993064

Zentralblatt MATH identifier
1260.35037

Citation

Aizicovici, Sergiu; Papageorgiou, Nikolaos S.; Staicu, Vasile. Multiple solutions for superlinear $p$-Laplacian Neumann problems. Osaka J. Math. 49 (2012), no. 3, 699--740. https://projecteuclid.org/euclid.ojm/1350306594

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