Results 131 to 140 of about 15,655 (167)

On growing solutions of nonlinear ordinary differential equations

Mathematical Notes, 1997
The author considers the solutions of an \(m\)th-order differential equation \[ w^{(m)}= Q(r,w, \dots, w^{(m-1)}), \] satisfying the condition: \[ w^{(m-i)}(r_*)> {t_*\over(i-1)!} r_*^{i-1}, \quad \text{for }i=1,2, \dots, m. \] If \(Q\) is a Carathéodory-type function on \([r_*,+\infty [\times \mathbb{R}^m\), such that for some \(k\in\{0,1, \dots, m-2\}
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Ordinary differential equations for nonlinear stochastic oscillators

Physics Letters A, 1988
Abstract The dynamics of a stochastic oscillator in the limit of small noise is studied by a cumulant expansion of the corresponding Fokker-Planck equation. A set of nonlinear first order differential equations for expectation values is obtained. To test our method the supercritical pitchfork bifurcation in a bistable potential is discussed.
Wolfram Just, Herwig Sauermann
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Nonlinear Ordinary Differential Equations: Problems and Solutions

2007
Abstract An ideal companion to the new 4th Edition of Nonlinear Ordinary Differential Equations by Jordan and Smith (OUP, 2007), this text contains over 500 problems and fully-worked solutions in nonlinear differential equations. With 272 figures and diagrams, subjects covered include phase diagrams in the plane, classification of ...
D W Jordan, P Smith
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An ordinary differential equation in nonlinear programming

Nonlinear Analysis: Theory, Methods & Applications, 1990
It is proved that the initial value problem of an ordinary differential equation \(x'=P(x,g'(x)),\quad x(0)=x_ 0,\) arising in nonlinear programming, has a unique solution under certain assumptions.
Hassan, Nizar, Rzymowski, Witold
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Singular solutions of nonlinear ordinary differential equations

Mathematical Notes, 1996
The author investigates the existence of singular solutions to the \(m\)th-order differential equation \[ y^{(m)}=Q(t,y,\dots,y^{(m-1)}).\tag{*} \] Conditions on the function \(Q\) are given which guarantee that every Kneser solution to (*) (i.e.
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Admissibility, dichotomies and nonlinear ordinary differential equations

Nonlinear Analysis: Theory, Methods & Applications, 1986
We determine a representation formula of the bounded (or tending to zero) solutions of the affine equation by a fundamental matrix of the homogeneous one (variation of constants formula). We examine the nonlinear equation and we prove the existence of bounded (or tending to zero) solutions under hypotheses similar to those of Carathéodory for the ...
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On factorization of nonlinear ordinary differential equations

Proceedings of the 1999 international symposium on Symbolic and algebraic computation, 1999
We give a decision procedure for existence of factorixations (tlec:ompositions int.0 lower order ODEs) of nonlinear orclinary differential cquat.ions y(“) = F(z: y(x), y’, . : y’“-“) for the general cast (,equations with arbitrary locally nieromorphic F). The prol)lcm of factorization for the CRSC of rational F is discussed.
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Bounded Solutions of Nonlinear Ordinary Differential Equations

1996
A classical result states that if A is a n × n real matrix and T > 0, then the system Open image in new window has a T-periodic solution for each T-periodic continuous forcing term p if and only if no eigenvalue of A has the form ikw with k ∈ ℤ and ω = 2π/T. The homogeneous part of equation (1) is then said to be non-resonant.
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Structural identification with physics-informed neural ordinary differential equations

Journal of Sound and Vibration, 2021
Zhilu Lai, Charilaos Mylonas, Satish Nagarajaiah   +2 more
exaly  

Nonlinear Ordinary Differential Equations

2016
Martin Hermann, Masoud Saravi
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