Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
difference equation; half-linear equation; functional; singular functional
difference equation; half-linear equation; functional; singular functional
Summary:
In the paper the discrete version of the Morse’s singularity condition is established. This condition ensures that the discrete functional over the unbounded interval is positive semidefinite on the class of the admissible functions. Two types of admissibility are considered.
References:
[1] Došlá Z., Došlý O.: Singular quadratic functionals of one dependent variable. Comment. Math. Univ. Carolinae 36 (1995), 219–237. MR 1357523 | Zbl 0838.34036
[2] Hartman P.: Ordinary differential equations. J. Wiley & Sons, New York, (1964). MR 0171038 | Zbl 0125.32102
[3] Kelley W. G., Peterson A. C.: Difference equations - An introduction with applications. Academic Press (1991). MR 1142573 | Zbl 0733.39001
[4] Leighton W.: Principal quadratic functionals. Trans. Amer. Math. Soc. 67 (1949), 253–274. MR 0034535 | Zbl 0041.22404
[5] Leighton W., Martin A. D.: Quadratic functionals with a singular end point. Trans. Amer. Math. Soc. 78 (1955), 98–128. MR 0066570 | Zbl 0064.35401
[6] Leighton W., Morse M.: Singular quadratic functionals. Trans. Amer. Math. Soc. 40 (1936), 252-286. MR 1501873 | Zbl 0015.02701
[7] Mařík R.: Nonnegativity of functionals corresponding to the second order half-linear differential equation. Arch. Math. (Brno) 35 (1999), 155–164. MR 1711728
[8] Mařík R.: Comparison theorems for half-linear second order difference equations. Arch. Math. (Brno) 36 (2000), 513–518. MR 1822821 | Zbl 1090.39500
[9] Řehák P.: Oscillatory properties of second order half–linear difference equations. Czech. Math. J. 51, No. 2 (2001), 303–321. MR 1844312
Search
Partner of
