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Second order nonlocal boundary value problems at resonance. (English) Zbl 1273.34029

Summary: We present sufficient conditions for the existence of positive solutions for some second-order boundary value problems at resonance. The boundary conditions that we study are quite general, involve a Stieltjes integral and include, as particular cases, multi-point and integral boundary conditions. Our results are based on a Leggett-Williams norm-type theorem due to O’Regan and Zima. We employ a general abstract approach which allows us to improve and complement recent results in the literature.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47H11 Degree theory for nonlinear operators
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