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November/December 2014 Nonlinear resonant periodic problems
Nikolaos S. Papageorgiou, Francesca Papalini
Differential Integral Equations 27(11/12): 1107-1146 (November/December 2014).

Abstract

We consider nonlinear periodic problems driven by the sum of a scalar $p$-Laplacian and a scalar Laplacian and a Carath\'{e}odory reaction, which at $\pm\infty$, is resonant with respect to any higher eigenvalue. Using variational methods, coupled with suitable perturbation and truncation techniques and Morse theory, we prove a three solutions theorem. For equations resonant with respect to the principal eigenvalue $\hat \lambda_0=0$, we establish the existence of nodal solutions.

Citation

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Nikolaos S. Papageorgiou. Francesca Papalini. "Nonlinear resonant periodic problems." Differential Integral Equations 27 (11/12) 1107 - 1146, November/December 2014.

Information

Published: November/December 2014
First available in Project Euclid: 18 August 2014

zbMATH: 1340.34062
MathSciNet: MR3263082

Subjects:
Primary: 34B15, 34B18, 34C25, 58E05

Rights: Copyright © 2014 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.27 • No. 11/12 • November/December 2014
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