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Zbl 0937.34025
Erbe, Lynn; Peterson, Allan; Mathsen, Ronald
Existence, multiplicity and nonexistence of positive solutions to a differential equation on a measure chain. (English)
[J] J. Comput. Appl. Math. 113, No.1-2, 365-380 (2000). ISSN 0377-0427

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.

MSC 2000:: *34B45 Boundary value problems on graphs and networks
34B15 Nonlinear boundary value problems of ODE

Keywords: existence; multiplicity; nonexistence; positive solutions; measure chain

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