Existence and uniqueness of nonlinear deflections of an infinite beam resting on a non-uniform nonlinear elastic foundation

Boundary value problems

Sung Woo Choi¹  Taek Soo Jang³ 

[1] Department of Mathematics, Duksung Womens'Department of Naval Architecture and Ocean Engineering, Pusan National University, Busan;s University, Seoul, Republic of Korea

关键词: Infinite beam;    elastic foundation;    nonlinear;    non-uniform;    fourth-order ordinary differential equation;    Banach fixed point theorem;    contraction.;   

DOI  :  10.1186/1687-2770-2012-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We consider the static deflection of an infinite beam resting on a nonlinear and non-uniform elastic foundation. The governing equation is a fourth-order nonlinear ordinary differential equation. Using the Green's function for the well-analyzed linear version of the equation, we formulate a new integral equation which is equivalent to the original nonlinear equation. We find a function space on which the corresponding nonlinear integral operator is a contraction, and prove the existence and the uniqueness of the deflection in this function space by using Banach fixed point theorem. 2010 Mathematics Subject Classification: 34A12; 34A34; 45G10; 74K10.

【 授权许可】

CC BY