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Existence of solutions of Sturm-Liouville boundary value problems for nonlinear second order impulsive differential equations in Banach spaces. (English) Zbl 0905.34019

Summary: A fixed point theorem is applied to investigate the existence of solutions to Sturm-Liouville boundary value problems for nonlinear second-order impulsive differential equations in Banach spaces.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34A37 Ordinary differential equations with impulses
34G20 Nonlinear differential equations in abstract spaces
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References:

[1] Guo Dajun, Existence of solutions of boundary value problems for nonlinear second order impulsive differential equations in Banach spaces, J.Math. Anal. Appl., 181, 2(1994),407–421. · Zbl 0807.34076 · doi:10.1006/jmaa.1994.1031
[2] Guo Dajun, Sun Jingxian, Nonlinear Integral Equations, Shandong Science and Technology Press, Jinan, 1986 (in Chinese). · Zbl 0596.45010
[3] Lakshmikantham, V., Bainov, D.D. and Simeonov, P.S., Theory of Impulsive Differential Equations. World Scientific, Singapore, 1989. · Zbl 0719.34002
[4] Lakshmikantham, V. and Leela, S.. Nonlinear Differential Equations in Abstract spaces, Pergamon, Oxford, 1981. · Zbl 0456.34002
[5] You Binli, A Supplement to Ordinary Differential Equations, Higher Education Press, Beijin, 1981 (in Chinese).
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