Electron. J. Diff. Eqns., Vol. 2006(2006), No. 96, pp. 1-10.

Existence, multiplicity and infinite solvability of positive solutions for p-Laplacian dynamic equations on time scales

Da-Bin Wang

Abstract:
In this paper, by using Guo-Krasnosel'skii fixed point theorem in cones, we study the existence, multiplicity and infinite solvability of positive solutions for the following three-point boundary value problems for $p$-Laplacian dynamic equations on time scales
$$\displaylines{ [ \Phi _p(u^{\triangle }(t))] ^{\triangledown}+a(t)f(t,u(t)) =0,\quad t\in [0,T]_{T}, \cr u(0)-B_0(u^{\triangle }(\eta )) = 0,\quad u^{\triangle }(T)=0. }$$
By multiplicity we mean the existence of arbitrary number of solutions.

Submitted April 14, 2006. Published August 22, 2006.
Math Subject Classifications: 34B10, 34B18, 39A10.
Key Words: Time scales; p-Laplacian; boundary value problem; positive solution; existence; multiplicity; infinite solvability.

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Da-Bin Wang
Department of Applied Mathematics
Lanzhou University of Technology
Lanzhou, Gansu, 730050, China
email: wangdb@lut.cn

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