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Systems of ordinary differential equations with nonlinear superposition principles
Physica D: Nonlinear Phenomena, 1982zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anderson, R. L. +2 more
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Asymptotic decomposition of systems of nonlinear ordinary differential equations
Ukrainian Mathematical Journal, 1984The construction of solutions of non linear ODE's by meams of asymptotic expansions relies on a relative-magnitude ordering of terms in the ODE's. This is most easily accomplished with the help of a 'small parameter'. Since usual small parameter expansions are not always successful, an alternate construction method is proposed.
Mitropol'skij, Yu. A., Lopatin, A. K.
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On the Existence of Periodic Solutions for a Nonlinear System of Ordinary Differential Equations
Acta Mathematica Sinica, English Series, 2000Consider the nonlinear system of ordinary differential equations \[ x^{(m)}(t)+A f(t,x(t),x'(t),\dots,x^{(m-1)}(t))=p(t), \] where \(x\in \mathbb{R}^n \), \(A \) is a nonsingular matrix, \(f \) is \(T \)-periodic with respect to the first variable, and \(p \) is \(T \)-periodic. The author obtains a Nagumo-type a priori bound for the periodic solutions
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On Nonlinear Systems of Ordinary Differential Equations
1988The paper gives some analytical representations and numerical methods for the solutions of systems of ordinary differential equations with emphasis of the formal side, using the connection to the linear partial differential equations in the case first mentioned.
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Nonlinear boundary-value problems for systems of ordinary differential equations
Ukrainian Mathematical Journal, 1998The author studies a boundary value problem for a system of nonlinear ordinary differential equations \[ (1)\quad \dot z=Z(z,t), \qquad (2) \quad lz= \varphi(z(\cdot)), \] where the nonlinear \(n\)-dimensional vector function \(Z(z,t)\) satisfies the conditions: \(Z( \cdot ,t)\in C^{1}[\|z-z_{0}\|\leq q]\) and \(Z(z, \cdot)\in C[a,b];\) \(l\) is a ...
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Exponential Dichotomy of Nonlinear Systems of Ordinary Differential Equations
1985Publisher Summary This chapter discusses exponential dichotomy of nonlinear systems of ordinary differential equations. A dichotomy, exponential or ordinary, is a type of conditional stability. A linear differential equation possesses a dichotomy if there exists an invariant splitting or a continuous decomposition of the Euclidean space into stable ...
S. Elaydi, O. Hajek
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Numerical Solution of the Coupled System of Nonlinear Fractional Ordinary Differential Equations
Advances in Applied Mathematics and Mechanics, 2017Summary: In this paper, we consider the numerical method that is proposed and analyzed in [\textit{J. Cao} and \textit{C. Xu}, J. Comput. Phys. 238, 154--168 (2013; Zbl 1286.65092)] for the fractional ordinary differential equations. It is based on the so-called block-by-block approach, which is a common method for the integral equations. We extend the
Zhou, Xiaojun, Xu, Chuanju
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A new approach for asymptotic stability system of the nonlinear ordinary differential equations
Journal of Applied Mathematics and Computing, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Effati, S., Nazemi, A. R.
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On the integration of a class of nonlinear systems of ordinary differential equations
AIP Conference Proceedings, 2017For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations.
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On the asymptotic behaviour of nonlinear systems of ordinary differential equations
Glasgow Mathematical Journal, 1985In this paper we study the asymptotic behaviour of the following systems of ordinary differential equations:where the identically zero function is a solution of (N) i.e. f(t, 0)=0 for all time t. Suppose one knows that all the solutions of (N) which start near zero remain near zero for all future time or even that they approach zero as time increases ...
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