## Abstract Utilizing the quadratic functional criteria and positive functionals, the author develops a comparison theorem for oscillation of partial differential equations. This result parallels a comparison of the oscillation of scalar ordinary differential equations to oscillation of vectorβmatr
Higher order non-resonance for differential equations with singularities
β Scribed by Ping Yan; Meirong Zhang
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 91 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.413
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β¦ Synopsis
Abstract
In this paper we prove an existence result of positive periodic solutions to second order differential equations with certain strong repulsive singularities near the origin and with some semilinear growth near infinity. Different from the nonsingular case, the result in this paper shows that both of the periodic and the antiperiodic eigenvalues play the same role in such an existence result. Copyright Β© 2003 John Wiley & Sons, Ltd.
π SIMILAR VOLUMES
In this paper, a non-variational version of a max-min principle is extended, and some unique existence results are obtained for the periodic boundary value problem of the higher order ordinary differential equations under a resonant condition.
The goal of this paper is to describe the set of polynomials r β C[x] such that the linear differential equation y = ry has Liouvillian solutions, where C is an algebraically closed field of characteristic 0. It is known that the differential equation has Liouvillian solutions only if the degree of
We obtain suffiaient conditions for the oscillation of all solutions of the higher order neutral differential equation -[?At) + P(t) YO -.)I + a t ) Y(t -0 ) = 0, t h to where Our results extend and improve several known results in the literature.