Differential and Integral Equations

Nonlinear resonant periodic problems

Nikolaos S. Papageorgiou and Francesca Papalini

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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.

Article information

Source
Differential Integral Equations, Volume 27, Number 11/12 (2014), 1107-1146.

Dates
First available in Project Euclid: 18 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1408366786

Mathematical Reviews number (MathSciNet)
MR3263082

Zentralblatt MATH identifier
1340.34062

Subjects
Primary: 34B15: Nonlinear boundary value problems 34B18: Positive solutions of nonlinear boundary value problems 34C25: Periodic solutions 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

Papageorgiou, Nikolaos S.; Papalini, Francesca. Nonlinear resonant periodic problems. Differential Integral Equations 27 (2014), no. 11/12, 1107--1146. https://projecteuclid.org/euclid.die/1408366786


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