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Zbl 1163.34300
Ma, Ruyun
A survey on nonlocal boundary value problems. (English)
[J] Appl. Math. E-Notes 7, 257-279, electronic only (2007). ISSN 1607-2510/e

In this survey, the author presents a collection of results on the existence and multiplicity of solutions for second order nonlocal boundary value problems (BVPs). In particular, the author illustrates some basic results present in literature on the following directions: solutions of BVPs without resonance, solutions of BVPs with resonance, positive solutions of multi-point BVPs, global continua of positive and nodal solutions of multi-point BVPs. The author also mentions some of the tools used to approach these types of problems and gives, at the end of the paper, a rich bibliography.
[Gennaro Infante (Arcavata di Rende)]

MSC 2000:: *34-02 Research monographs (ordinary differential equations)
34B10 Multipoint boundary value problems
34B15 Nonlinear boundary value problems of ODE
34B18 Positive solutions of nonlinear boundary value problems

Keywords: Nonlocal boundary value problem; Positive solutions; Nodal solutions; Resonance

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