Geodesic
Existence of positive solutions for singular four-point boundary value problem with a $p$-Laplacian
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 957-973.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper we deal with the four-point singular boundary value problem $$ \begin {cases} (\phi _p(u'(t)))'+q(t)f(t,u(t),u'(t))=0, t\in (0,1),\\ u'(0)-\alpha u(\xi )=0, \quad u'(1)+\beta u(\eta )=0, \end {cases} $$ where $\phi _p(s)=|s|^{p-2}s$, $p>1$, $0\xi \eta 1$, $\alpha ,\beta >0$, $q\in C[0,1]$, $q(t)>0$, $t\in (0,1)$, and $f\in C([0,1]\times (0,+\infty )\times \mathbb R,(0,+\infty ))$ may be singular at $u = 0$. By using the well-known theory of the Leray-Schauder degree, sufficient conditions are given for the existence of positive solutions.
Classification : 34B10, 34B16, 34B18
Keywords: singular; four-point; positive solution; $p$-Laplacian 
@article{CMJ_2009__59_4_a6,
     author = {Miao, Chunmei and Zhao, Junfang and Ge, Weigao},
     title = {Existence of positive solutions for singular four-point boundary value problem with a $p${-Laplacian}},
     journal = {Czechoslovak Mathematical Journal},
     pages = {957--973},
     publisher = {mathdoc},
     volume = {59},
     number = {4},
     year = {2009},
     mrnumber = {2563569},
     zbl = {1224.34053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a6/}
}
TY  - JOUR
AU  - Miao, Chunmei
AU  - Zhao, Junfang
AU  - Ge, Weigao
TI  - Existence of positive solutions for singular four-point boundary value problem with a $p$-Laplacian
JO  - Czechoslovak Mathematical Journal
PY  - 2009
SP  - 957
EP  - 973
VL  - 59
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a6/
LA  - en
ID  - CMJ_2009__59_4_a6
ER  - 
%0 Journal Article
%A Miao, Chunmei
%A Zhao, Junfang
%A Ge, Weigao
%T Existence of positive solutions for singular four-point boundary value problem with a $p$-Laplacian
%J Czechoslovak Mathematical Journal
%D 2009
%P 957-973
%V 59
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a6/
%G en
%F CMJ_2009__59_4_a6
Miao, Chunmei; Zhao, Junfang; Ge, Weigao. Existence of positive solutions for singular four-point boundary value problem with a $p$-Laplacian. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 957-973. http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a6/