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Zbl 1069.34018
Sun, Yongping; Liu, Lishan
Solvability for a nonlinear second-order three-point boundary value problem. (English)
[J] J. Math. Anal. Appl. 296, No. 1, 265-275 (2004). ISSN 0022-247X

Using the Leray-Schauder nonlinear alternative theory, a nonconstant solution is found under suitable new conditions for the following three-point BVP $$u'' +f(t,u)=0,\quad 0<t<1, \quad u'(0)=0, u(1)=\alpha u(\eta),$$ with $0<\eta<1$ and $\alpha>0$ or $\alpha<0$. Some examples are given to illustrate the results.
[Yujun Dong (Nanjing)]

MSC 2000:: *34B10 Multipoint boundary value problems
34B15 Nonlinear boundary value problems of ODE

Keywords: second-order nonlinear ordinary differential equation; three point boundary value problem; Leray-Schauder nonlinear alternative

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