EXISTENCE OF A POSITIVE SOLUTION FOR A FIRST-ORDER <i>P</i>-LAPLACIAN BVP WITH IMPULSIVE ON TIME SCALES

Lijian Yin; Zhiyu Zhang

doi:10.11948/2012007

2012 Volume 2 Issue 1

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Lijian Yin, Zhiyu Zhang. EXISTENCE OF A POSITIVE SOLUTION FOR A FIRST-ORDER P-LAPLACIAN BVP WITH IMPULSIVE ON TIME SCALES[J]. Journal of Applied Analysis & Computation, 2012, 2(1): 103-109. doi: 10.11948/2012007

Citation:

Lijian Yin, Zhiyu Zhang. EXISTENCE OF A POSITIVE SOLUTION FOR A FIRST-ORDER P-LAPLACIAN BVP WITH IMPULSIVE ON TIME SCALES[J]. Journal of Applied Analysis & Computation, 2012, 2(1): 103-109. doi: 10.11948/2012007

EXISTENCE OF A POSITIVE SOLUTION FOR A FIRST-ORDER P-LAPLACIAN BVP WITH IMPULSIVE ON TIME SCALES

Lijian Yin¹,
Zhiyu Zhang²

1 Department of Mathematics, North University of China, Taiyuan, Shanxi, 030008, China;
2 Taiyuan Institute of Technology Taiyuan, Shanxi, 030008, China

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Abstract

Abstract

In this paper, we consider the existence of a positive solution for a first-order p-Laplacian BVP with impulsive on time scales:ϕ_p(y^∆(t))=h(t)f(y(t)) t ∈[0, T]_T\{τ}, Imp(y(τ))=Iy(t), y(0)=B₀(T). Using the fixed-point theory, we have established the problem in a Banach space with an appropriate operator. Our main contribution is to the combination of the first-order p-Laplacian BVP and the impulsive dynamic equation. We obtained some new results which have advanced recent developments on this type of problem.
- Time scales /
- p-Laplacian operator /
- the fixed theory /
- cone
MSC: 34B18;34B37

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References

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