Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 58, pp. 1-15.

Title: Existence and uniqueness of nontrivial solutions for nonlinear
       higher-order three-point eigenvalue problems on time scales
 
Authors: Wei Han     (North Univ. of China, Taiyuan, China)
         Yonggui Kao (Harbin Institute of Technology, China)

Abstract: 
 In this paper, we study a nonlinear higher-order three-point
 eigenvalue problems with first-order derivative on time scales.
 Under certain growth conditions on the nonlinearity, sufficient
 conditions for  existence and uniqueness of nontrivial solutions,
 which are easily verifiable, are obtained by using the
 Leray-Schauder nonlinear alternative.
 The conditions used in the paper are different from those
 in [4, 10, 21]. To show  applications of our main results,
 we present some examples.
 
Submitted November 6, 2007. Published April 17, 2008.
Math Subject Classifications: 39A10, 34B15, 34B18.
Key Words: Time scale; nontrivial solutions; eigenvalue problem;
           fixed point theorem; Leray-Schauder nonlinear alternative.