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Existence of periodic and subharmonic solutions for second-order superlinear difference equations. (English) Zbl 1215.39001

Summary: By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations \(\Delta^{2} x_{n - 1} + f(n, x_{n} ) = 0\), some new results are obtained for the above problems when \(f(t, z)\) has superlinear growth at zero and at infinity in \(z\).

MSC:

39A05 General theory of difference equations
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