Abstract
In this paper, we investigate the existence of positive solutions for nonlinear multipoint boundary value problems for p-Laplacian dynamic equations on time scales with the delta derivative of the nonlinear term. Sufficient assumptions are obtained for existence of at least twin or arbitrary even positive solutions to some boundary value problems. Our results are achieved by appealing to the fixed point theorems of Avery-Henderson. As an application, an example to demonstrate our results is given.
Highlights
The theory of dynamic equation on time scales was pioneered by Stefan Hilger in his Ph.D. thesis in 1988
By using the five functionals fixed-point theorem, they showed that the boundary value problem (BVP) has at least three positive solutions
We study the following p -Laplacian multipoint BVPs on time scales (φp(u∆(t)))∇ + a(t)f (t, u(t), u∆(t)) = 0, t ∈ [0, T ]T, (1.1)
Summary
The theory of dynamic equation on time scales was pioneered by Stefan Hilger in his Ph.D. thesis in 1988[12] as a process of combining construction for the research of differential equations in the continuous situation and research of finite difference equations in the discontinuous situation. In [6], Dogan investigated the following p-Laplacian multipoint boundary value problem (BVP) on time scales (φp(u∆(t)))∇ + a(t)f (t, u(t)) = 0, t ∈ (0, T )T, m−2 u(0) = aiu(ξi), i=1 m−2 φp(u∆(T )) = biφp(u∆(ξi)). By using the five functionals fixed-point theorem, they showed that the BVP has at least three positive solutions.
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