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

• Main Authors: Wei Han, Yonggui Kao
• Format: Article
• Language: English
• Published: Texas State University 2008-04-01
• Series: Electronic Journal of Differential Equations
• Subjects: Time scale; nontrivial solutions; eigenvalue problem; fixed point theorem; Leray-Schauder nonlinear alternative
• Online Access: http://ejde.math.txstate.edu/Volumes/2008/58/abstr.html
• ISSN: 1072-6691

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.