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Multiple Solutions for Nonlinear Periodic Problems

Published online by Cambridge University Press:  20 November 2018

Sophia Th. Kyritsi
Affiliation:
Department of Mathematics, Hellenic Naval Academy, Piraeus 18539, Greece e-mail: [email protected]
Nikolaos S. Papageorgiou
Affiliation:
National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece e-mail: [email protected]
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Abstract

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We consider a nonlinear periodic problem driven by a nonlinear nonhomogeneous differential operator and a Carathéodory reaction term $f\left( t,\,x \right)$ that exhibits a $\left( p\,-\,1 \right)$-superlinear growth in $x\,\in \,\mathbb{R}$ near $\pm \infty $ and near zero. A special case of the differential operator is the scalar $p$-Laplacian. Using a combination of variational methods based on the critical point theory with Morse theory (critical groups), we show that the problem has three nontrivial solutions, two of which have constant sign (one positive, the other negative).

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2013

References

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