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Zeitschrift für Analysis und ihre Anwendungen


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Volume 36, Issue 3, 2017, pp. 253–281
DOI: 10.4171/ZAA/1588

Published online: 2017-07-17

Superlinear, Noncoercive Asymmetric Robin Problems with Indefinite, Unbounded Potential

Nikolaos S. Papageorgiou[1] and Vicenţiu D. Rădulescu[2]

(1) National Technical University, Athens, Greece
(2) King Abdulaziz University, Jeddah, Saudi Arabia, and University of Craiova, Romania

We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential. The reaction term exhibits an asymmetric behavior, namely it is superlinear in the positive direction but without satisfying the Ambrosetti–Rabinowitz condition and it is sublinear but noncoercive in the negative direction. Using variational methods together with suitable truncation and perturbation techniques and Morse theory (critical groups), we prove a multiplicity theorem producing three nontrivial smooth solutions two of which have constant sign (one positive and the other negative).

Keywords: Superlinear reaction term, asymmetric nonlinearity, constant sign solutions, critical groups, C-condition, mountain pass theorem, indefinite potential, Robin boundary condition

Papageorgiou Nikolaos, Rădulescu Vicenţiu: Superlinear, Noncoercive Asymmetric Robin Problems with Indefinite, Unbounded Potential. Z. Anal. Anwend. 36 (2017), 253-281. doi: 10.4171/ZAA/1588