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September 2012 Multiple solutions for superlinear $p$-Laplacian Neumann problems
Sergiu Aizicovici, Nikolaos S. Papageorgiou, Vasile Staicu
Osaka J. Math. 49(3): 699-740 (September 2012).

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).

Citation

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Sergiu Aizicovici. Nikolaos S. Papageorgiou. Vasile Staicu. "Multiple solutions for superlinear $p$-Laplacian Neumann problems." Osaka J. Math. 49 (3) 699 - 740, September 2012.

Information

Published: September 2012
First available in Project Euclid: 15 October 2012

zbMATH: 1260.35037
MathSciNet: MR2993064

Subjects:
Primary: 35J25, 35J70, 58E05

Rights: Copyright © 2012 Osaka University and Osaka City University, Departments of Mathematics

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Vol.49 • No. 3 • September 2012
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