Unbounded solutions of third order three-point boundary value problems on a half-line

Advances in Nonlinear Analysis

article

Ravi P. Agarwal¹  Erbil Çetin² 

[1] Department of Mathematics, Texas A&M University–Kingsville, 700 University Blvd.;Department of Mathematics, Ege University

关键词: Three-point boundary value problem;    lower and upper solutions;    half-line;    Schauder's fixed point theorem;    topological degree theory;   

DOI  :  10.1515/anona-2015-0043

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We consider the following third order three-point boundary value problem on a half-line: x '''( t )+ q ( t ) f ( t , x ( t ), x '( t ), x ''( t )) = 0, t ∈ (0,+∞), x '(0) = A , x (η) = B , x ''(+∞) = C , where η ∈ (0,+∞), but fixed, and f : [0,+∞) × ℝ 3 → ℝ satisfies Nagumo's condition. We apply Schauder's fixed point theorem, the upper and lower solution method, and topological degree theory, to establish existence theory for at least one unbounded solution, and at least three unbounded solutions. To demonstrate the usefulness of our results, we illustrate two examples.

【 授权许可】

CC BY