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Multiple nonnegative solutions for second order impulsive differential equations. (English) Zbl 1047.34008
Using a combination of the Leray-Schauder alternative and Krasnosel’skij’s fixed-point theorem in cones, the authors study the existence of single and multiple solutions to a second-order impulsive equation with fixed moments. One theorem deals with the existence only, while the second and third theorem are concerned with the existence of two nonnegative solutions and their localization.

34A37Differential equations with impulses
34B18Positive solutions of nonlinear boundary value problems for ODE
Full Text: DOI
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[2] R.P. Agarwal, D. O’Regan, P.J.Y. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer, Dordrecht, 1999
[3] Eloe, P. W.; Henderson, J.: Positive solutions of boundary value problems for ordinary differential equations with impulse. Dynamics of continuous, discrete and impulsive systems 4, 285-294 (1998) · Zbl 0903.34013
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[8] Guo, D.: Existence of solutions of boundary value problems for nonlinear second order impulsive differential equations in Banach spaces. Jour. math. Anal. appl. 181, 407-421 (1994) · Zbl 0807.34076
[9] Guo, D.; Liu, X.: Multiple positive solutions of boundary value problems for impulsive differential equations. Nonlinear anal. 25, 327-337 (1995) · Zbl 0840.34015
[10] D. O’Regan, Existence Theory for Nonlinear Ordinary Differential Equations, Kluwer, Dordrecht, 1997