## Solvability of Second Order Delta-Nabla p-Laplacian m-point Eigenvalue Problem on Time Scales

## Solvability of Second Order Delta-Nabla p-Laplacian m-point Eigenvalue Problem on Time Scales

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*S. N. Rao*

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## Abstract

In this paper, we are concerned with the following eigenvalue problem of m-point boundary value problem for p-Laplacian dynamic equation on time scales, ()∇ () ϕp(u ∆(t))+ λh(t)fu(t)=0,t ∈ [a, b]T, m−2 ∑ u(a) − u ∆(a)= u ∆(ξi),u ∆(b)=0,m ≥ 3, i=1 where ϕp(u)= |u|p−2u,p > 1 and λ> 0 is a real parameter. Under certain assumptions, some new results on existence of one or two positive solutions and nonexistence are obtained for λ evaluated in diﬀerent intervals by using Guo-Krasnosel’skii ﬁxed point theorem.

## Keywords

eigenvalue, time scale, p-Laplacian, positive solution, ﬁxed point, cone.