Existence of three positive solutions to a second-order boundary value problem on a measure chain

Authors:
Richard I. Avery;Douglas R. Anderson
Affiliations:
College of Natural Sciences, Dakota State University, Madison, SD;Department of Mathematics and Computer Science, Concordia College, Moorhead, MN
Venue:
Journal of Computational and Applied Mathematics - Dynamic equations on time scales
Year:
2002

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Abstract

Growth conditions are imposed on f such that the boundary value problem -xΔΔ(t)= f(xσ(t)), t ∈ [t1, t2], λx(t1) - ηxΔ(t1) = 0 and µx(σ(t2)) + δxΔ(σ(t2)) = 0, where t1 t2 from a measure chain T, has at least three positive solutions by way of the five functionals fixed point theorem.