Existence of multiple solutions to a discrete fourth order periodic boundary value problem Abstract References Full Text (384.1K)
John R. Graef - 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.
Received: July 2012; Revised: December 2012; Published: November 2013. |