Author:
Çetin Erbil,Topal Fatma Serap,Agarwal Ravi P.
Abstract
AbstractLet$\mathbb{T}\subseteq \mathbb{R}$T⊆Rbe a time scale. The purpose of this paper is to present sufficient conditions for the existence of multiple positive solutions of the following Lidstone boundary value problem on time scales:$$\begin{aligned} &(-1)^{n} y^{\Delta ^{(2n)}}(t) = f\bigl(t, y(t)\bigr), \quad \text{$t\in [a,b]_{ \mathbb{T}}$,} \\ &y^{\Delta ^{(2i)}}(a)= y^{\Delta ^{(2i)}}\bigl(\sigma ^{2n-2i}(b)\bigr)=0,\quad i=0,1,\ldots,n-1. \end{aligned}$$(−1)nyΔ(2n)(t)=f(t,y(t)),t∈[a,b]T,yΔ(2i)(a)=yΔ(2i)(σ2n−2i(b))=0,i=0,1,…,n−1.Existence of multiple positive solutions is established using fixed point methods. At the end some examples are also given to illustrate our results.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
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