Geodesic
Existence and uniqueness of solutions to a super-linear three-point boundary-value problem
Electronic journal of differential equations, Tome 2005 (2005)
In previous papers, degree theory for nonlinear operators has been used to study a class of three-point boundary-value problems for second order ordinary differential equations having a super-linear term, and existence of a sequence of solutions has been shown. In this paper, we forgo the previous approach for the shooting method, which gives a drastically simpler existence theory, with less assumptions, and easy calculation of solutions. We even obtain uniqueness in the simplest case.
Classification : 34B10, 34B15
Keywords: super-linear, three-point boundary-value problem 
@article{EJDE_2005__2005__a196,
     author = {Calvert,  Bruce and Gupta,  Chaitan P.},
     title = {Existence and uniqueness of solutions to a super-linear three-point boundary-value problem},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1075.34011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a196/}
}
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%A Gupta,  Chaitan P.
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Calvert,  Bruce; Gupta,  Chaitan P. Existence and uniqueness of solutions to a super-linear three-point boundary-value problem. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a196/