Existence of solutions to nonlinear problems with three-point boundary conditions. (English) Zbl 1360.34038

Dallos Santos, Dionicio Pastor

Electron. J. Differ. Equ. 2017, Paper No. 35, 10 p. (2017).

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

MSC:

34B10	Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations
47H10	Fixed-point theorems
47H11	Degree theory for nonlinear operators

Keywords:

boundary value problems; Schauder fixed point theorem; Leray-Schauder degree; lower and upper solutions

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