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Existence of periodic and subharmonic solutions for second-order superlinear difference equations

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Abstract

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.

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Correspondence to Jianshe Yu.

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Guo, Z., Yu, J. Existence of periodic and subharmonic solutions for second-order superlinear difference equations. Sci. China Ser. A-Math. 46, 506–515 (2003). https://doi.org/10.1007/BF02884022

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  • DOI: https://doi.org/10.1007/BF02884022

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