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).

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

Summary: 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 
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     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},
     publisher = {mathdoc},
     volume = {2006},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a69/}
}
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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/