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Existence of positive solutions for multi-point boundary value problems on infinite intervals in Banach spaces. (English) Zbl 1258.34046

Summary: We investigate the positive solutions of a class of second-order nonlinear singular differential equations with multi-point boundary value conditions on an infinite interval in Banach spaces. The tools we used are the cone theory and Mönch fixed point theorem and a monotone iterative technique. An example is also given to demonstrate the applications of our results, which include and extend some existing results.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34G20 Nonlinear differential equations in abstract spaces
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B40 Boundary value problems on infinite intervals for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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