Asymptotic Behavior of the Potential and Existence of a Periodic Solution for a Second Order Differential Equation

Authors

Alfonso Castro, Harvey Mudd CollegeFollow
Chen Chang, University of Texas at San Antonio

Document Type

Article - postprint

Department

Mathematics (HMC)

Publication Date

11-2003

Abstract

We establish the existence of a 2π-periodic solution for a second order semilinear equation in terms of the asymptotic behavior of the potential of the nonlinearity. Our condition includes the case in which the nonlinearity is asymptotically linear with slopes at infinity of the jumping nonlinearity between the positive axes and the first Fucik spectrum curve (see [S. Fucik (1976). Boundary value problems with jumping nonlinearities. Casopis Pest. Mat., 101, 69–87.]). Our results extend those of [L. Fernandez and F. Zanolin (1988). Periodic solutions of a second order differential equation with one-sided growth restriction on the restoning term. Arch. Math., 51, 151–163.].

Comments

Author's post-print manuscript available for download.

For the publisher's PDF, please visit http://dx.doi.org/10.1080/0003681031000154918

Rights Information

© 2003 Taylor & Francis

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Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1080/0003681031000154918

Recommended Citation

Castro, Alfonso and Chen Chang. “Asymptotic behavior of the potential and existence of a periodic solution for a second order differential equation”, Applicable Analysis, Vol. 82, No. 11, November 2003, pp. 1029-1038.