Abstract
In this paper, we consider the existence of homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity. The classical Ambrosetti-Rabinowitz superlinear condition is improved by a general superlinear one. The proof is based on the critical point theory in combination with periodic approximations of solutions.
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Supported by Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT1226), National Natural Science Foundation of China (Grant Nos. 11171078 and 11031002) and the Specialized Fund for the Doctoral Program of Higher Education of China (Grant No. 20114410110002)
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Zhou, Z., Yu, J.S. Homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity. Acta. Math. Sin.-English Ser. 29, 1809–1822 (2013). https://doi.org/10.1007/s10114-013-0736-0
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DOI: https://doi.org/10.1007/s10114-013-0736-0
Keywords
- Homoclinic solution
- periodic nonlinear difference equation
- superlinear nonlinearity
- critical point theory
- periodic approximation