Geodesic
On positive solutions for a nonlinear boundary value problem with impulse
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 247-265
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.
In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.
Classification : 34A37, 34B15, 34B18, 34B37, 47N20
Keywords: impulse conditions; Green’s function; completely continuous operator; fixed point theorem in cones 
@article{CMJ_2006_56_1_a14,
     author = {Bereketoglu, Huseyin and Huseynov, Aydin},
     title = {On positive solutions for a nonlinear boundary value problem with impulse},
     journal = {Czechoslovak Mathematical Journal},
     pages = {247--265},
     year = {2006},
     volume = {56},
     number = {1},
     mrnumber = {2207016},
     zbl = {1164.34371},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006_56_1_a14/}
}
TY  - JOUR
AU  - Bereketoglu, Huseyin
AU  - Huseynov, Aydin
TI  - On positive solutions for a nonlinear boundary value problem with impulse
JO  - Czechoslovak Mathematical Journal
PY  - 2006
SP  - 247
EP  - 265
VL  - 56
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2006_56_1_a14/
LA  - en
ID  - CMJ_2006_56_1_a14
ER  - 
%0 Journal Article
%A Bereketoglu, Huseyin
%A Huseynov, Aydin
%T On positive solutions for a nonlinear boundary value problem with impulse
%J Czechoslovak Mathematical Journal
%D 2006
%P 247-265
%V 56
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2006_56_1_a14/
%G en
%F CMJ_2006_56_1_a14
Bereketoglu, Huseyin; Huseynov, Aydin. On positive solutions for a nonlinear boundary value problem with impulse. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 1, pp. 247-265. http://geodesic.mathdoc.fr/item/CMJ_2006_56_1_a14/

[1] F. M. Atici and G. Sh. Guseinov: On the existence of positive solutions for nonlinear differential equations with periodic boundary conditions. J. Comput. Appl. Math. 132 (2001), 341–356. | DOI | MR

[2] D. D. Bainov and P. S. Simeonov: Impulsive Differential Equations: Asymtotic Properties of the Solutions. World Scientific, Singapore, 1995. | MR

[3] P. W. Eloe and J. Henderson: Positive solutions of boundary value problems for ordinary differential equations with impulse. Dynam. Contin. Discrete Impuls. Systems 4 (1998), 285–294. | MR

[4] P. W. Eloe and M. Sokol: Positive solutions and conjugate points for a boundary value problem with impulse. Dynam. Systems Appl. 7 (1998), 441–449. | MR

[5] L. H. Erbe, S. Hu and H. Wang: Multiple positive solutions of some boundary value problems. J. Math. Anal. Appl. 184 (1994), 640–648. | DOI | MR

[6] L. H. Erbe and H. Wang: On the existence of positive solutions of ordinary differential equations. Proc. Amer. Math. Soc. 120 (1994), 743–748. | DOI | MR

[7] D. Guo and V. Lakshmikantham: Nonlinear Problems in Abstract Cones. Academic Press, San Diego, 1998. | MR

[8] M. A. Krasnosel’skii: Positive Solutions of Operator Equations. Noordhoff, Groningen, 1964. | MR

[9] M. A. Neumark: Lineare Differential Operatoren. Akademie-Verlag, Berlin, 1967.

[10] A. M. Samoilenko and N. A. Perestyuk: Impulsive Differential Equations. World Scientific, Singapore, 1995. | MR

[11] Š. Schwabik, M. Tvrdý and O. Vejvoda: Differential and Integral Equations: Boundary Value Problems and Adjoint. Academia and Reidel, Praha and Dordrecht, 1979. | MR

[12] Š. Schwabik: Generalized Ordinary Differential Equations. World Scientific, Singapore, 1992. | MR | Zbl

[13] M. Tvrdý: Differential and integral equations in the space of regulated functions. Memoirs on Differential Equations and Mathematical Physics 25 (2002), 1–104. | MR

[14] M. Tvrdý: Linear distributional differential equations of the second order. Math. Bohem. 119 (1994), 415–436. | MR