Geodesic
Existence and non-existence of positive solutions of four-point BVPs for second order ordinary differential equations on whole line
Novi Sad Journal of Mathematics, Tome 46 (2016) no. 1.

Voir la notice de l'article provenant de la source Novi sad journal of mathematics website

This paper is concerned with four-point boundary value problems of second order singular differential equations on whole lines. The Green's function $G(t,s)$ for the problem $$\begin{array}{l} -(\rho(t)x'(t))'=0,\lim\limits_{t\to-\infty}\rho(t)x'(t)-kx(\xi)=\lim\limits_{t\to +\infty}\rho(t)x'(t)+l x(\eta)=0 \end{array} $$ is obtained. We proved that $G(t,s)\ge 0$ under some assumptions which actually generalizes a corresponding result in [Appl. Math. Comput. 217(2)(2010) 811-819]. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established.
Publié le :
DOI : 10.30755/NSJOM.02415
Classification : 34B10, 34B15, 35B10
Keywords: second order singular differential equation on whole line, four-point boundary value problem, positive solution, fixed point theorem 
@article{10.30755/NSJOM.02415,
     author = {Yuji Liu and Xiaohui Yang},
     title = {Existence and non-existence of positive solutions of four-point {BVPs} for
second order ordinary differential equations on whole line},
     journal = {Novi Sad Journal of Mathematics},
     pages = {79 - 103},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2016},
     doi = {10.30755/NSJOM.02415},
     url = {http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.02415/}
}
TY  - JOUR
AU  - Yuji Liu
AU  - Xiaohui Yang
TI  - Existence and non-existence of positive solutions of four-point BVPs for
second order ordinary differential equations on whole line
JO  - Novi Sad Journal of Mathematics
PY  - 2016
SP  - 79 
EP  -  103
VL  - 46
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.02415/
DO  - 10.30755/NSJOM.02415
ID  - 10.30755/NSJOM.02415
ER  - 
%0 Journal Article
%A Yuji Liu
%A Xiaohui Yang
%T Existence and non-existence of positive solutions of four-point BVPs for
second order ordinary differential equations on whole line
%J Novi Sad Journal of Mathematics
%D 2016
%P 79 - 103
%V 46
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.02415/
%R 10.30755/NSJOM.02415
%F 10.30755/NSJOM.02415
Yuji Liu; Xiaohui Yang. Existence and non-existence of positive solutions of four-point BVPs for
second order ordinary differential equations on whole line. Novi Sad Journal of Mathematics, Tome 46 (2016) no. 1. doi : 10.30755/NSJOM.02415. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.02415/

Cité par Sources :