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Homoclinic solutions of a class of nonperiodic discrete nonlinear systems in infinite higher dimensional lattices. (English) Zbl 1470.39029

Summary: By using critical point theory, we obtain a new sufficient condition on the existence of homoclinic solutions of a class of nonperiodic discrete nonlinear systems in infinite lattices. The classical Ambrosetti-Rabinowitz superlinear condition is improved by a general superlinear one. Some results in the literature are improved.

MSC:

39A22 Growth, boundedness, comparison of solutions to difference equations
34A33 Ordinary lattice differential equations
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
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