Existence of Positive Solutions form-Point Boundary Value Problems on Time Scales | Zendy

Ying Zhang | Zendy; Qiao Shi-dong | Zendy

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Existence of Positive Solutions form-Point Boundary Value Problems on Time Scales

Author(s) -

Ying Zhang,

Qiao Shi-dong

Publication year - 2009

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2009/189768

Subject(s) - fixed point theorem , mathematics , fixed point , boundary value problem , boundary (topology) , scale (ratio) , combinatorics , value (mathematics) , point (geometry) , laplace operator , discrete mathematics , mathematical analysis , statistics , physics , geometry , quantum mechanics

We study the one-dimensional p-Laplacian m-point boundary value problem (φp(uΔ(t)))Δ+a(t)f(t,u(t))=0, t∈[0,1]T, u(0)=0, u(1)=∑i=1m−2aiu(ξi), where T is a time scale, φp(s)=|s|p−2s, p>1, some new results are obtained for the existence of at least one, two, and threepositive solution/solutions of the above problem by using Krasnosel′skll′s fixed point theorem, new fixed point theorem due to Avery and Henderson, as well asLeggett-Williams fixed point theorem. This is probably the first time the existence of positivesolutions of one-dimensional p-Laplacian m-point boundary value problem on time scales has been studied

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