×

zbMATH — the first resource for mathematics

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.

MSC:
34A37 Ordinary differential equations with impulses
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Agarwal, R.P.; O’Regan, D., Positive solutions for (p, n-p) conjugate boundary value problems, Jour. differential eqns., 150, 462-473, (1998) · Zbl 0920.34027
[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
[4] Erbe, L.H.; Krawcewicz, W., Existence of solutions to boundary value problems for impulsive second order differential inclusions, Rocky mountain J. math., 22, 1-20, (1992) · Zbl 0784.34012
[5] Erbe, L.H.; Hu, S.; Wang, H., Multiple positive solutions of some boundary value problems, Jour. math. anal. appl., 184, 640-648, (1994) · Zbl 0805.34021
[6] Frigon, M.; O’Regan, D., Boundary value problems for second order impulsive differential equations using set-valued maps, Appl. anal., 58, 325-333, (1995) · Zbl 0831.34008
[7] Gatica, J.A.; Oliker, V.; Waltman, P., Iterative procedures for nonlinear second order boundary value problems, Ann. mat. pura appl., 157, 1-25, (1989) · Zbl 0729.34013
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.