Generalized zeros and nonpositivity of energy functionals associated with half-linear even order difference equations

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Authors

DOŠLÝ Ondřej

Year of publication 2015
Type Article in Proceedings
Conference Difference equations, discrete dynamical systems and applications
MU Faculty or unit

Faculty of Science

Citation
Web http://dx.doi.org/10.1007/978-3-319-24747-2_6
Doi http://dx.doi.org/10.1007/978-3-319-24747-2_6
Field General mathematics
Keywords Generalized zero; energy functional; focal point; even order half-linear difference equation
Description We investigate the relationship between oscillatory properties of half-linear even order difference equations and nonpositivity of the associated energy functionals. We convert the investigated difference equation into a Hamiltonian type difference system and using this transformation we establish our main result which says that the existence of two (or more) generalized zeros of a solution of the investigated difference equation implies that the corresponding energy functional attains a nonpositive value.
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