`a`

Existence of multiple solutions to a discrete fourth order periodic boundary value problem

Pages: 291 - 299, Issue special, November 2013

 Abstract        References        Full Text (384.1K)              

John R. Graef - Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States (email)
Lingju Kong - Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States (email)
Min Wang - Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States (email)

Abstract: Sufficient conditions are obtained for the existence of multiple solutions to the discrete fourth order periodic boundary value problem \begin{equation*} \begin{array}{l} \Delta^4 u(t-2)-\Delta(p(t-1)\Delta u(t-1))+q(t) u(t)=f(t,u(t)),\quad t\in [1,N]_{\mathbb{Z}},\\ \Delta^iu(-1)=\Delta^iu(N-1),\quad i=0, 1,2, 3. \end{array} \end{equation*} Our analysis is mainly based on the variational method and critical point theory. One example is included to illustrate the result.

Keywords:  Discrete boundary value problem, fourth order, multiple solutions, critical points, variational methods.
Mathematics Subject Classification:  Primary: 39A10; Secondary: 34B15.

Received: July 2012;      Revised: December 2012;      Published: November 2013.

 References