Electron. J. Diff. Eqns., Vol. 2008(2008), No. 58, pp. 1-15.

Existence and uniqueness of nontrivial solutions for nonlinear higher-order three-point eigenvalue problems on time scales

Wei Han, Yonggui Kao

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.

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Wei Han
Department of Mathematics, North University of China
Taiyuan Shanxi, 030051, China
email: qd_hanweiwei1@126.com
  Yonggui Kao
Department of Mathematics, Harbin Institute of Technology
Weihai Shandong 264209, China
email: kaoyonggui@sina.com

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