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International Journal of Mathematics and Mathematical Sciences
Volume 23, Issue 11, Pages 783-788

Existence and uniqueness theorems for some fourth-order nonlinear boundary value problems

Department of Mathematics, Northwest Normal University, Gansu, Lanzhou 730070, China

Received 30 March 1998

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let G and f:[0,1]×4 be two functions satisfying Caratheodory conditions. This paper is concerned with the problems of existence and uniqueness of solutions for the nonlinear fourth-order ordinary differential equation y+λy+ky+G(x,y,y,y,y)=f(x,y,y,y,y) with one of a particular set of boundary conditions.