Generalized zeros and nonpositivity of energy functionals associated with half-linear even order difference equations
| Authors | |
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| Year of publication | 2015 |
| Type | Article in Proceedings |
| Conference | Difference equations, discrete dynamical systems and applications |
| MU Faculty or unit | |
| Citation | DOŠLÝ, Ondřej. Generalized zeros and nonpositivity of energy functionals associated with half-linear even order difference equations. In M. Bohner, Z. Ding, O. Došlý. Difference equations, discrete dynamical systems and applications. Berlin: Springer, 2015, p. 82-93. ISBN 978-3-319-24745-8. Available from: https://dx.doi.org/10.1007/978-3-319-24747-2_6. |
| 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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