MULTIPLICITY RESULTS FOR A CLASS OF SECOND ORDER SUPERLINEAR DIFFERENCE SYSTEMS

Title & Authors
MULTIPLICITY RESULTS FOR A CLASS OF SECOND ORDER SUPERLINEAR DIFFERENCE SYSTEMS
Zhang, Guoqing; Liu, Sanyang;

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 $\small{(P)\{{\Delta}^2x(k-1)+g(k,y(k))=0,\;k{\in}[1,\;T],\;{\Delta}^2y(k-1)+f(k,\;x(k)=0,\;k{\in}[1,\;T],\;x(0)=y(0)=0,\;x(T+1)=y(T+1)=0}$ where T is a positive integer, [1, T] is the discrete interval {1, 2,..., T}, $\small{{\Delat}x(k)=x(k+1)-x(k)}$ is the forward difference operator and $\small{{\Delta}^2x(k)={\Delta}({\Delta}x(k))}$.
Keywords
difference systems;multiple;critical point theory;super-linear;
Language
English
Cited by
1.
Nontrivial solutions for resonant difference systems via computations of the critical groups, Journal of Mathematical Analysis and Applications, 2012, 385, 1, 60
2.
Nontrivial solutions of a second order difference systems with multiple resonance, Applied Mathematics and Computation, 2012, 218, 18, 9342
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