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Multiplicity results for a class of second order superlinear difference systems

Guoqing Zhang|Sanyang Liu
대한수학회 (The Korean Mathematical Society)|2006.11|대한수학회보 (Bulletin of the KMS)|제43권 제4호|pp. 693-701

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Abstract

Using Minimax principle and Linking theorem in crit-ical point theory, we prove the existence of two nontrivial solutionsfor the following second order superlinear dierence systems(P)8<:2x(k 1) + g(k;y(k)) = 0; k2 [1;T];2y(k 1) + f(k;x(k)) = 0; k2 [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 intervalf1;2;:;Tg; x(k) = x(k + 1) x(k) is the forward dierence operator and42x(k) = 4 (4 x(k)).

참고문헌 (4)

  1. "Di？？erence equations and inequalities", 228 (2000), Marcel Dekker Inc.
  2. "Multiple positive solutions of singularand nonsingular discrete problems via variational methods", 58(1-2), pp.69~73 (2004)
  3. "The existence of periodic and subharmonic solutions fora class of second order superlinear, di？？erence equation", 33, pp.226~235 (2003)
  4. "Minimax methods in critical point theory with applications todi？？erential equations CBMS Regional Conference Series in Mathematics", 65 (1986)

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