Abstract
We present sufficient conditions for the existence of at least twin or triple positive solutions of a nonlinear four-point singular boundary value problem with a -Laplacian dynamic equation on a time scale. Our results are obtained via some new multiple fixed point theorems.
Highlights
Let T be a closed nonempty subset of R
We introduce the sets Tk and Tk which are derived from the time scale T as follows
This paper is concerned with the multiplicity of positive solutions for the following nonlinear four-point singular boundary value problem of a p-Lapalcian dynamic equation on a time scale φp uΔ t ∇ atfut 0, t ∈ 0, 1 T, 1.6
Summary
Let T be a closed nonempty subset of R. This paper is concerned with the multiplicity of positive solutions for the following nonlinear four-point singular boundary value problem of a p-Lapalcian dynamic equation on a time scale φp uΔ t ∇ atfut 0, t ∈ 0, 1 T, m1φp u 0 − n1φp uΔ ξ. Some authors have studied the existence of multiple positive solutions for the nonlinear second-order three-point boundary value problems on time scales, for instance, Anderson 7 has proved that the problem uΔ∇ t f t, u t 0, u 0 0, au η u T. By using fixed point theorems due to Avery and Henderson 12 , Avery and Peterson 14 , respectively, we prove that there exist at least twin or triple positive solutions to problems 1.6.
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