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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:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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