Abstract and Applied Analysis

An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction

Yongxiang Li and He Yang

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Abstract

We discuss the solvability of the fourth-order boundary value problem u ( 4 ) = f ( t , u , u ′′ ) , 0 t 1 , u ( 0 ) = u ( 1 ) = u ′′ ( 0 ) = u ′′ ( 1 ) = 0 , which models a statically bending elastic beam whose two ends are simply supported, where f : [ 0,1 ] × R 2 R is continuous. Under a condition allowing that f ( t , u , v ) is superlinear in u and v , we obtain an existence and uniqueness result. Our discussion is based on the Leray-Schauder fixed point theorem.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 694590, 9 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620725

Digital Object Identifier
doi:10.1155/2010/694590

Mathematical Reviews number (MathSciNet)
MR2660384

Zentralblatt MATH identifier
1360.34044

Citation

Li, Yongxiang; Yang, He. An Existence and Uniqueness Result for a Bending Beam Equation without Growth Restriction. Abstr. Appl. Anal. 2010 (2010), Article ID 694590, 9 pages. doi:10.1155/2010/694590. https://projecteuclid.org/euclid.aaa/1288620725


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