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Positive solutions for nonlinear three-point boundary value problems on time scales. (English) Zbl 1070.34029
The authors generalize some known results on positive solutions of a three-point boundary value problem related to the dynamic equation \[ u^{\Delta\nabla} (t) + a(t) f(t,u(t)) = 0. \] The symbol \(\Delta\nabla\) denotes the natural Laplace operator on time scales (arbitrary closed subsets of the reals). The methods used in the proofs are based on Leggett–Williams/ Krasnoselskii fixed-point techniques in cones.

MSC:
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
39A12 Discrete version of topics in analysis
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