Boundary value problems | |
Existence and uniqueness of nonlinear deflections of an infinite beam resting on a non-uniform nonlinear elastic foundation | |
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
【 预 览 】
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