Geodesic
Multiple positive solutions for singular $m$-point boundary-value problems with nonlinearities depending on the derivative
Electronic Journal of Differential Equations, Tome 2008 (2008).

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

Summary: Using the fixed point theorem in cones, this paper shows the existence of multiple positive solutions for the singular $$\displaylines{ x''(t)+a(t)f(t,x(t),x'(t))=0,\quad 01,\cr x'(0)=0,\quad x(1)= \sum_{i=1}^{m-2}a_{i}x(\xi_i), }$$ where $0\xi_1\xi_2\dots\xi_{m-2}1, a_i\in [0,1), i = 1, 2,\dots, m-2$, with $0 \sum_{i=1}^{m-2}a_i 1 $ and $f$ maybe singular at $x=0$ and $x'=0$.
Classification : 34B10, 34B15
Keywords: m-point boundary-value problem, singularity, positive solutions, fixed point theorem 
@article{EJDE_2008__2008__a87,
     author = {Ma, Ya and Yan, Baoqiang},
     title = {Multiple positive solutions for singular $m$-point boundary-value problems with nonlinearities depending on the derivative},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2008},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a87/}
}
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Ma, Ya; Yan, Baoqiang. Multiple positive solutions for singular $m$-point boundary-value problems with nonlinearities depending on the derivative. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a87/