By using Riccati transformation, new oscillation criteria are given for forced second order differential equations with mixed nonlinearities, which improve and generalize results in the literature. An (ฮฑ + 1)-degree functional is involved for oscillation, which is widely used in variational theories
Oscillation criteria for first and second order forced difference equations with mixed nonlinearities
โ Scribed by Ravi P. Agarwal; Martin Bohner; Wing-Sum Cheung; Said R. Grace
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 227 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0895-7177
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โฆ Synopsis
Some new criteria for the oscillation of certain difference equations with mixed nonlinearities are established. The main tool in the proofs is an inequality due to Hardy, Littlewood, and Pรณlya.
๐ SIMILAR VOLUMES
In this paper, some new oscillation criteria are obtained for the first-order delay difference equation k k Xn+I-x,~+ (k+l)k+l xn\_kรทf(n,x,~\_l~,...,xn\_t~) =0, n=0,1,2,..., where k,/1,/2,..., ls are positive integer numbers, f is a function. Our results improve the known results in the literature.
By using the Riccati technique and the variational principle, new oscillation criteria are given for second-order quasi-linear differential equations with an oscillatory forcing term, which improve and generalize some new results from the literature. An (ฮฑ + 1)-degree functional is involved in the o
Some new sufficient conditions for the oscillation criteria are given for the forced second-order nonlinear differential equations with delayed argument in the form, ## โข " (t) + q (t) f (z (~-(t))) = e (t) The results are based on the information only on a sequence of subintervals of [to, oc) ra