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Solvability of Sturm-Liouville boundary value problems with impulses

Li Zhang*, Xiankai Huang and Chunfeng Xing

Author Affiliations

Department of Foundation Courses, Beijing Union University, Beijing, 100101, China

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Boundary Value Problems 2013, 2013:192  doi:10.1186/1687-2770-2013-192

Published: 28 August 2013


In this paper, we consider a kind of Sturm-Liouville boundary value problems with impulsive effects. By using the mountain pass theorem and Ekeland’s variational principle, the existence of two positive solutions and two negative solutions is established. Moreover, we do not assume that the nonlinearity satisfies the well-known AR-condition.

MSC: 34B15, 34B37, 58E30.

p-Laplacian; boundary value problem; variational; impulsive