Differential and Integral Equations

Degree theoretic methods in the study of nonlinear periodic problems with nonsmooth potentials

Ravi P. Agarwal, Michael E. Filippakis, Donal O'Regan, and Nikolaos S. Papageorgiou

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In this paper we study periodic problems driven by the scalar ordinary $p$-Laplacian and with a nonsmooth potential. Using degree theoretic methods based on a fixed-point index for nonconvex-valued multifunctions, we prove two existence theorems. In the first we employ nonuniform nonresonance conditions between two successive eigenvalues of the negative $p$-Laplacian with periodic boundary conditions. In the second we use Landesman-Lazer conditions.

Article information

Differential Integral Equations, Volume 19, Number 3 (2006), 279-296.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34A60: Differential inclusions [See also 49J21, 49K21]
Secondary: 34B15: Nonlinear boundary value problems 34B18: Positive solutions of nonlinear boundary value problems


Agarwal, Ravi P.; Filippakis, Michael E.; O'Regan, Donal; Papageorgiou, Nikolaos S. Degree theoretic methods in the study of nonlinear periodic problems with nonsmooth potentials. Differential Integral Equations 19 (2006), no. 3, 279--296. https://projecteuclid.org/euclid.die/1356050514

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