Abstract and Applied Analysis

Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations

Ying Wu and Guodong Han

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Abstract

Several new existence theorems on positive, negative, and sign-changing solutions for the following fourth-order beam equation are obtained: u ( 4 ) = f ( t , u ( t ) ) ,   t [ 0 , 1 ] ;   u ( 0 ) = u ( 1 ) = u ′′ ( 0 ) = u ′′ ( 1 ) = 0 , where f C ( [ 0 , 1 ] × 1 , 1 ) . In particular, an infinitely many sign changing solution theorem is established. The method of the invariant set of decreasing flow is employed to discuss this problem.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 635265, 11 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511900

Digital Object Identifier
doi:10.1155/2013/635265

Mathematical Reviews number (MathSciNet)
MR3055971

Zentralblatt MATH identifier
1277.34023

Citation

Wu, Ying; Han, Guodong. Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations. Abstr. Appl. Anal. 2013 (2013), Article ID 635265, 11 pages. doi:10.1155/2013/635265. https://projecteuclid.org/euclid.aaa/1393511900


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