## Abstract and Applied Analysis

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

#### Abstract

Several new existence theorems on positive, negative, and sign-changing solutions for the following fourth-order beam equation are obtained: ${u}^{\left(4\right)}=f\left(t,u\left(t\right)\right)$,   $t\in \left[0,1\right]$;  $u\left(0\right)=u\left(1\right)={u}^{\prime \prime }\left(0\right)={u}^{\prime \prime }\left(1\right)=0$, where $f\in C\left(\left[0,1\right]×{ℝ}^{1},{ℝ}^{1}\right)$. 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

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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