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Zbl 0763.34009
Gupta, Chaitan P.
Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation.
(English)
[J] J. Math. Anal. Appl. 168, No.2, 540-551 (1992). ISSN 0022-247X

The paper deals with the second order three-point nonlinear boundary value problem (1) $u''=f(x,u(x),u'(x))-e(x)$, $0<x<1$, $u(0)=0$, $u(\eta)=u(1)$, where $f$ is a Carathéodory function and $e$ is a Lebesgue integrable function. Provided $f$ has at most linear growth in its phase variables, the author establishes conditions for the existence of solutions to (1) and for the uniqueness of problem (1). The proofs are based on the topological degree theory and the Leray-Schauder continuation theorem. A priori estimates are obtained by Wirtinger-type inequalities.
[I.Rachuunková (Olomouc)]
MSC 2000:
*34B10 Multipoint boundary value problems
34B15 Nonlinear boundary value problems of ODE

Keywords: second order three-point nonlinear boundary value problem; existence; uniqueness; topological degree; Leray-Schauder continuation theorem; Wirtinger-type inequalities

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