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Zbl 1121.34023
Kosmatov, Nickolai
A multi-point boundary value problem with two critical conditions. (English)
[J] Nonlinear Anal., Theory Methods Appl. 65, No. 3, A, 622-633 (2006). ISSN 0362-546X

A coincidence degree theorem due to Mawhin is applied to show the existence of a solution to the multipoint boundary value problem for the nonlinear second-order equation $$ u''=f(t,u,u') , \qquad t \in (0,1)\,,$$ $$ u'(0)= u'(\eta)\,, \qquad u(1)=\sum^{n}_{i=1}\alpha_{i} u(\eta_{i})\,,$$ where $\,0< \eta \leq 1,\, \sum^{n}_{i=1}\alpha_{i}=\sum^{n}_{i=1}\alpha_{i} \eta_{i} =1\, $ and $f$ satisfies the Caratheodory conditions. Sufficient conditions are given in order to prove the existence of at least one solution. Both boundary conditions are responsible for resonance.
[Carmen Simerská (Praha)]

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

Keywords: Multipoint boundary value problem; Coincidence degree theorem; Resonance

Cited in: Zbl 1127.34006

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