Abstract
This paper is concerned with the existence and nonexistence of positive solutions of the -Laplacian functional dynamic equation on a time scale, , , , , , . We show that there exists a such that the above boundary value problem has at least two, one, and no positive solutions for and , respectively.
Highlights
Let T be a closed nonempty subset of R, and let T have the subspace topology inherited from the Euclidean topology on R
We are concerned with the existence of positive solutions of the p-Laplacian dynamic equation on a time scale φp xΔ t ∇ λa t f x t, x μ t
Our results show that the number of positive solutions of 1.1 is determined by the parameter λ
Summary
This paper is concerned with the existence and nonexistence of positive solutions of the p-Laplacian functional dynamic equation on a time scale, φp x t ∇ λa t f x t , x u t. We show that there exists a λ∗ > 0 such that the above boundary value problem has at least two, one, and no positive solutions for 0 < λ < λ∗, λ λ∗ and λ > λ∗, respectively.
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