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Existence of positive solutions for singular semipositone \((k, n-k)\) conjugate \(m\)-point boundary value problems. (Chinese. English summary) Zbl 1463.34103

Summary: By constructing a special cone and using the fixed point theorem concerning cone compression and expansion in norm type, the existence of positive solution is obtained in the paper for \(m\)-point boundary value problem of the higher order super-linear differential system, in which the nonlinear term is singular and semipositone. The results obtained in this paper essentially improve and generalize many well known results.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
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