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MULTIPLICITY RESULTS FOR A CLASS OF SECOND ORDER SUPERLINEAR DIFFERENCE SYSTEMS

  • Zhang, Guoqing (COLLEGE OF SCIENCE, UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY) ;
  • Liu, Sanyang (COLLEGE OF SCIENCE, XIDIAN UNIVERSITY)
  • Published : 2006.11.30

Abstract

Using Minimax principle and Linking theorem in critical point theory, we prove the existence of two nontrivial solutions for the following second order superlinear difference systems $$(P)\{{\Delta}^2x(k-1)+g(k,y(k))=0,\;k{\in}[1,\;T],\;{\Delta}^2y(k-1)+f(k,\;x(k)=0,\;k{\in}[1,\;T],\;x(0)=y(0)=0,\;x(T+1)=y(T+1)=0$$ where T is a positive integer, [1, T] is the discrete interval {1, 2,..., T}, ${\Delat}x(k)=x(k+1)-x(k)$ is the forward difference operator and ${\Delta}^2x(k)={\Delta}({\Delta}x(k))$.

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Cited by

  1. Nontrivial solutions for resonant difference systems via computations of the critical groups vol.385, pp.1, 2012, https://doi.org/10.1016/j.jmaa.2011.06.027
  2. Nontrivial solutions of a second order difference systems with multiple resonance vol.218, pp.18, 2012, https://doi.org/10.1016/j.amc.2012.03.017