3,390 research outputs found
Generating Finite Dimensional Integrable Nonlinear Dynamical Systems
In this article, we present a brief overview of some of the recent progress
made in identifying and generating finite dimensional integrable nonlinear
dynamical systems, exhibiting interesting oscillatory and other solution
properties, including quantum aspects. Particularly we concentrate on Lienard
type nonlinear oscillators and their generalizations and coupled versions.
Specific systems include Mathews-Lakshmanan oscillators, modified Emden
equations, isochronous oscillators and generalizations. Nonstandard Lagrangian
and Hamiltonian formulations of some of these systems are also briefly touched
upon. Nonlocal transformations and linearization aspects are also discussed.Comment: To appear in Eur. Phys. J - ST 222, 665 (2013
Oscillation Criteria for Second‐Order Neutral Damped Differential Equations with Delay Argument
The chapter is devoted to study the oscillation of all solutions to second‐order nonlinear neutral damped differential equations with delay argument. New oscillation criteria are obtained by employing a refinement of the generalized Riccati transformations and integral averaging techniques
Asymptotic Behavior of Even-Order Damped Differential Equations with p-Laplacian like Operators and Deviating Arguments
We study the asymptotic properties of the solutions of a class of even-order damped differential equations with p-Laplacian like operators, delayed and advanced arguments. We present new theorems that improve and complement related contributions reported in the literature. Several examples are provided to illustrate the practicability, maneuverability, and efficiency of the results obtained. An open problem is proposed
The oscillatory behavior of second order nonlinear elliptic equations
Some oscillation criteria are established for the nonlinear damped elliptic differential equation of second order
which are different from most known ones in the sense that they are based on a new weighted function defined in the sequel. Both the cases when exists for all and when it does not exist for some are considered
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