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Positive solutions for a nonlinear differential equation on a measure chain. (English) Zbl 0963.34020
Summary: The authors are concerned with proving the existence of positive solutions to general two-point boundary value problems for the nonlinear equation $$Lx(t):= -[r(t) x^\Delta(t)]^\Delta= f(t, x(t)).$$ They use fixed-point theorems concerning cones in a Banach space. Important results concerning Green functions for general two-point boundary value problems for $$Lx(t):= -[r(t) x^\Delta(t)]^\Delta= 0$$ are given.

MSC:
34B18Positive solutions of nonlinear boundary value problems for ODE
34A34Nonlinear ODE and systems, general
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References:
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