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Multiple and Nodal Solutions for a Class of Nonlinear, Nonhomogeneous Periodic Eigenvalue Problems

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Abstract

We consider a nonlinear parametric periodic problem driven by a nonhomogeneous differential operator. We assume that the reaction is (p \(-\) 1)-superlinear near \({\pm }\infty \) (without satisfying the AR-condition) and exhibits concave terms near the origin. We show the existence of five nontrivial solutions providing sign information for all of them.

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Acknowledgments

The author wishes to thank a knowledgeable referee for his/her corrections and remarks that improved the paper considerably.

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  1. Hellenic Naval Academy, Hatzikyriakou Avenue, 18539, Piraeus, Greece

    Evgenia H. Papageorgiou

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  1. Evgenia H. Papageorgiou
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Correspondence to Evgenia H. Papageorgiou.

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Papageorgiou, E.H. Multiple and Nodal Solutions for a Class of Nonlinear, Nonhomogeneous Periodic Eigenvalue Problems. Differ Equ Dyn Syst 24, 499–517 (2016). https://doi.org/10.1007/s12591-016-0287-9

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  • DOI: https://doi.org/10.1007/s12591-016-0287-9

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