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Existence of anti-periodic solutions for second-order ordinary differential equations involving the Fučík spectrum

Xin Zhao1 and Xiaojun Chang2*

Author Affiliations

1 College of Information Technology, Jilin Agricultural University, Changchun, 130118, P.R. China

2 College of Mathematics, Jilin University, Changchun, Jilin, 130012, China

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Boundary Value Problems 2012, 2012:149  doi:10.1186/1687-2770-2012-149

Published: 21 December 2012


In this paper, we study the existence of anti-periodic solutions for a second-order ordinary differential equation. Using the interaction of the nonlinearity with the Fučík spectrum related to the anti-periodic boundary conditions, we apply the Leray-Schauder degree theory and the Borsuk theorem to establish new results on the existence of anti-periodic solutions of second-order ordinary differential equations. Our nonlinearity may cross multiple consecutive branches of the Fučík spectrum curves, and recent results in the literature are complemented and generalized.

anti-periodic solutions; Fučík spectrum; Leray-Schauder degree theory; Borsuk theorem