Geodesic
A necessary and sufficient condition for the existence of positive solutions to singular boundary-value problems of higher order differential equations
Electronic journal of differential equations, Tome 2006 (2006)
By constructing some special cones and using fixed point theorem of cone expansion and compression, this paper presents some necessary and sufficient conditions for the existence of $C^{4n-2}$ positive solutions to a class of singular boundary-value problems. Some examples are presented to illustrate our main results.
Classification : 34B16
Keywords: singular sublinear boundary-value problem, positive solution, fixed point theorem, cone, higher order differential equation 
@article{EJDE_2006__2006__a69,
     author = {Zhao,  Chenglong and Yuan,  Yanyan and Liu,  Yansheng},
     title = {A necessary and sufficient condition for the existence of positive solutions to singular boundary-value problems of higher order differential equations},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1120.34011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a69/}
}
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%J Electronic journal of differential equations
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%F EJDE_2006__2006__a69
Zhao,  Chenglong; Yuan,  Yanyan; Liu,  Yansheng. A necessary and sufficient condition for the existence of positive solutions to singular boundary-value problems of higher order differential equations. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a69/