Topological Methods in Nonlinear Analysis

Existence and multiplicity of solutions for resonant nonlinear Neumann problems

Sergiu Aizicovici, Nikolaos S. Papageorgiou, and Vasile Staicu

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Abstract

We consider nonlinear Neumann problems driven by the $p$-Laplacian differential operator with a Caratheodory nonlinearity. Under hypotheses which allow resonance with respect to the principal eigenvalue $\lambda_{0}=0$ at $\pm\infty$, we prove existence and multiplicity results. Our approach is variational and uses critical point theory and Morse theory (critical groups).

Article information

Source
Topol. Methods Nonlinear Anal., Volume 35, Number 2 (2010), 235-252.

Dates
First available in Project Euclid: 21 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461251005

Mathematical Reviews number (MathSciNet)
MR2676815

Zentralblatt MATH identifier
1203.35116

Citation

Aizicovici, Sergiu; Papageorgiou, Nikolaos S.; Staicu, Vasile. Existence and multiplicity of solutions for resonant nonlinear Neumann problems. Topol. Methods Nonlinear Anal. 35 (2010), no. 2, 235--252. https://projecteuclid.org/euclid.tmna/1461251005


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References

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