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Existence, multiplicity and nonexistence of positive solutions to a differential equation on a measure chain. (English) Zbl 0937.34025
Summary: The authors are concerned with proving the existence of one or more than one positive solution of a general two-point boundary value problem for the nonlinear equation $$Lx(t):= -[p(t)x^\Delta(t)]^\Delta+ q(t) x^\sigma(t)= \lambda a(t) f(t,x^\sigma(t)).$$ They obtain criteria which lead to nonexistence of positive solutions. Here, the independent variable $t$ is in a “measure chain”. For proving they use fixed point theorems for operators on a Banach space.

34B45Boundary value problems for ODE on graphs and networks
34B15Nonlinear boundary value problems for ODE
Full Text: DOI
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