Geodesic
Positive and monotone solutions of an $m$-point boundary-value problem
Electronic Journal of Differential Equations, Tome 2002 (2002).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the second-order ordinary differential equation $$ y''(t)=-f(t,y(t),y'(t)),\quad 0\leq t\leq 1, $$ subject to the multi-point boundary conditions $$ \alpha y(0)\pm \beta y'(0)=0,\quad y(1)=\sum_{i=1}^{m-2}\alpha_iy(\xi_i)\,. $$ We prove the existence of a positive solution (and monotone in some cases) under superlinear and/or sublinear growth rate in $f$. Our approach is based on an analysis of the corresponding vector field on the $(y,y')$ face-plane and on Kneser's property for the solution's funnel.
Classification : 34B10, 34B18, 34B15
Keywords: multipoint boundary value problems, positive monotone solution, vector field, sublinear, superlinear, kneser's property, solution's funel 
@article{EJDE_2002__2002__a240,
     author = {Palamides, Panos K.},
     title = {Positive and monotone solutions of an $m$-point boundary-value problem},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a240/}
}
TY  - JOUR
AU  - Palamides, Panos K.
TI  - Positive and monotone solutions of an $m$-point boundary-value problem
JO  - Electronic Journal of Differential Equations
PY  - 2002
VL  - 2002
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a240/
LA  - en
ID  - EJDE_2002__2002__a240
ER  - 
%0 Journal Article
%A Palamides, Panos K.
%T Positive and monotone solutions of an $m$-point boundary-value problem
%J Electronic Journal of Differential Equations
%D 2002
%V 2002
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a240/
%G en
%F EJDE_2002__2002__a240
Palamides, Panos K. Positive and monotone solutions of an $m$-point boundary-value problem. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a240/