Electron. J. Differential Equations, Vol. 2017 (2017), No. 35, pp. 1-10.

Existence of solutions to nonlinear problems with three-point boundary conditions

Dionicio Pastor Dallos Santos

Using Leray-Schauder degree theory and the method of upper and lower solutions, we obtain a solution for nonlinear boundary-value problem
 \big(\varphi(u' )\big)'= f(t,u,u') \cr
where l(u,u')=0 denotes the three-point boundary conditions on [0,T], and $\varphi$ is a homeomorphism such that $\varphi(0)=0$.

Submitted September 21, 2016. Published January 30, 2017.
Math Subject Classifications: 34B15, 34B16, 47H10, 47H11.
Key Words: Boundary value problems; Schauder fixed point theorem; Leray-Schauder degree; lower and upper solutions.

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Dionicio Pastor Dallos Santos
Department of Mathematics, IME-USP
Cidade Universitária
CEP 05508-090, São Paulo, SP, Brazil
email: dionicio@ime.usp.br

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