# American Institute of Mathematical Sciences

2003, 2003(Special): 313-319. doi: 10.3934/proc.2003.2003.313

## A three point boundary value problem containing the operator

 1 Department of Mathematics, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago 2 Centro de Modelamiento Matemático and Departamento de Ingenieria Matemática, F.C.F.M, Universidad de Chile, Casilla 170, Correo 3, Santiago

Received  September 2002 Revised  February 2003 Published  April 2003

We consider problems of the form

$(\phi(u'))' = f(t, u, u'), t \in (0, 1)$;

under the three point boundary condition

$u'(0) = 0, u(n) = u(1);$

where $n \in$ (0, 1) is given. This problem is at resonance. Three-point boundary value problems at resonance have been studied in several papers, we present here some new result as well as generalizations of some results valid for particular forms of the operator -$(\phi(u'))'. Citation: Marta García-Huidobro, Raul Manásevich. A three point boundary value problem containing the operator. Conference Publications, 2003, 2003 (Special) : 313-319. doi: 10.3934/proc.2003.2003.313  [1] Corentin Audiard. On the non-homogeneous boundary value problem for Schrödinger equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 3861-3884. doi: 10.3934/dcds.2013.33.3861 [2] Shenghao Li, Min Chen, Bing-Yu Zhang. A non-homogeneous boundary value problem of the sixth order Boussinesq equation in a quarter plane. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2505-2525. doi: 10.3934/dcds.2018104 [3] Laurent Denis, Anis Matoussi, Jing Zhang. 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