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Homoclinic orbits for second order nonlinear \(p\)-Laplacian difference equations. (English. Russian original) Zbl 1302.39010

J. Contemp. Math. Anal., Armen. Acad. Sci. 46, No. 3, 172-182 (2011); translation from Izv. Nats. Akad. Nauk Armen., Mat. 46, No. 3, 17-28 (2011).
Summary: The paper proves the existence of nontrivial homoclinic orbits for second order nonlinear \(p\)-Laplacian difference equations without assumptions on periodicity using the critical point theory. Moreover, if the nonlinearity is an odd function, the existence of an unbounded sequence of nontrivial homoclinic orbits is proved.

MSC:

39A12 Discrete version of topics in analysis
37C29 Homoclinic and heteroclinic orbits for dynamical systems
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
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