×

Solutions of impulsive boundary value problems on the half-line. (English) Zbl 0912.34021

The paper is devoted to find sufficient conditions to guarantee the existence of positive solutions to a class of second-order nonlinear integro-differential equations with impulses and boundary conditions on the half-line. Using fixed point theory on cones, the author proves two results on the existence of positive solutions. Moreover, in the first one it is demonstrated that the determined solution is bounded.
Some examples are presented to illustrate the main theorems and to show that such results improve previous works in this direction.
Reviewer: Eduardo Liz (Vigo)

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34A37 Ordinary differential equations with impulses
45J05 Integro-ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Chen, Shaozhu; Zhang, Yong, Singular boundary value problems on a half-line, J. Math. Anal. Appl., 195, 449-468 (1995) · Zbl 0852.34019
[2] Kawano; Yanagida; Yotsutani, Structure theorems for positive radial solutions to Δ \(uKx u^p =0 in\textit{R^n\) · Zbl 0793.34024
[3] Junyu, Tan, The radial solutions of 2-order semilinear elliptic equations, Acta Math. Appl. Sinica, 19, 57-64 (1996) · Zbl 0864.35040
[4] Granas, A.; Guerther, R. B.; Lee, J. W.; O’Regan, D., Boundary value problems on infinite intervals and semiconductor devices, J. Math. Anal. Appl., 116, 335-348 (1986) · Zbl 0594.34019
[5] Baxley, J. V., Existence and uniqueness for nonlinear boundary value problems on infinite intervals, J. Math. Anal. Appl., 147, 127-133 (1990) · Zbl 0719.34037
[6] Guo, D.; Liu, X. Z., Impulsive integro-differential equations on unbounded domain in a Banach space, Nonlinear Studies, 3, 49-57 (1996) · Zbl 0864.45009
[7] Guo, D.; Liu, X., Multiple positive solutions of boundary value problems for impulsive differential equations, Nonlinear Anal., 25, 327-337 (1995) · Zbl 0840.34015
[8] Liu, Xiyu, Some existence and nonexistence principles for a class of singular boundary value problems, Nonlinear Anal., 27, 1147-1164 (1996) · Zbl 0860.34010
[10] Ladde, G. S.; Lakshmikantham, V.; Vatsala, A. S., Monotone Iterative Technique for Nonlinear Differential Equations (1985), Pitman Advanced Publishing Program: Pitman Advanced Publishing Program London · Zbl 0658.35003
[11] Deimling, K., Nonlinear Functional Analysis (1985), Springer-Verlag: Springer-Verlag Berlin · Zbl 0559.47040
[12] Bobisud, L. E., Existence of positive solutions to some nonlinear singular boundary value problems on finite and infinite intervals, J. Math. Anal. Appl., 173, 69-83 (1993) · Zbl 0777.34017
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.