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Applied Mathematics Letters, 2002 The author studies the differential system \(v'(t)+mv(t)+[p(v)](t)\leq 0\) with \(v(0)-v(T)\leq 0\). The main results conclude \(v(t)\leq 0\) for appropriate applications \(p:L^1([0,T])\to L^1([0,T])\) and real constants \(m\). A typical hypothesis states the existence of a real constant \(n\) such that \(n\min_{t\in[0,\tau]}v(t)\leq \text{ess}\inf_{t ...
J J Nieto
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Singularly Perturbed Linear Stochastic Ordinary Differential Equations
SIAM Journal on Mathematical Analysis, 1979Singularly perturbed linear differential equations with random forcing functions have recently been studied as models of control and filtering systems. The analysis in these studies has been somewhat formal, and important properties of the boundary layer behavior have been neglected as a consequence.
Blankenship, G., Sachs, S.
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Class of Perturbation Theories of Ordinary Differential Equations
Journal of Mathematical Physics, 1971A class of perturbation theories of ordinary differential equations is studied in a systematic and rigorous way. This class contains the perturbation theory by Kruskal [J. Math. Phys. 3, 806 (1962)] and its generalization discussed by Coffey [J. Math. Phys.
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Regular Perturbation of Ordinary Differential Equations
2015In this chapter we find asymptotic solutions of regularly perturbed equations and systems of equations, to which problems in mechanics are reduced. We consider Cauchy problems, problems for periodic solutions and boundary value problems.
S. M. Bauer +4 more
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2. Singularly Perturbed Ordinary Differential Equations
Studies in Applied Mathematics, 1995exaly +2 more sources
Some perturbation problems in ordinary differential equations
Funkcialaj Ekvacioj, 1967The author considers the differential equation \[ x' = f(t,x) + G(t) \] on \(\mathbb R^1\times \mathbb R^n\) where \(R(t,x) + G(t)\) is the perturbing part. It is shown that the existence of a positively bounded and exponentially stable solution is not affected by the perturbing terms if \(R(t,0)=0\), \(\vert R(t,x) - R(t,y)\vert \le k\,\vert x - y ...
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Singularly Perturbed Linear Ordinary Differential Equations
2015In this chapter, we study systems of linear differential equations with variable coefficients.
S. M. Bauer +4 more
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Asymptotic Stability for Ordinary Differential Equations with Delayed Perturbations
SIAM Journal on Mathematical Analysis, 1974Asymptotic stability of the zero solution of \[\dot x(t) = - a(t)x(t) + P(t,x_t )\] is studied with a direct method of Razumikhin. If $| {P(t,\varphi )} | \leqq \alpha (t)\theta \| \varphi \|$ for some $\theta < 1$, and $a(t) \geqq \alpha > 0$, then zero is exponentially stable; if the condition on $a(t)$ is weakened to $a(t) \geqq 0$ and $\int ^\
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Exponential methods for singularly perturbed ordinary differential–difference equations
Applied Mathematics and Computation, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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SINGULAR PERTURBATIONS OF ORDINARY DIFFERENTIAL EQUATIONS
1961Abstract : A discussion is presented concerning the perturbation method for ordinary differential equations with a small parameter epsilon. As illustrations of this procedure, use of the Neumann series and the Fredholm expansion is made. The solution of the eigenvalue problem is made for an ordinary differential equation as a power series in epsilon.
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