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A survey on nonlocal boundary value problems. (English) Zbl 1163.34300

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.

MSC:
34-02Research monographs (ordinary differential equations)
34B10Nonlocal and multipoint boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE