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Nonlinear singularly perturbed problems of ultra parabolic equations
Applied Mathematics and Mechanics, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lin, Surong, Mo, Jiaqi
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Bifurcation singularities of a singularly perturbed equation with delay
Siberian Mathematical Journal, 1999The singularly perturbed equation with delay of the form \[ \varepsilon \frac{dx}{dt}+x(t-\varepsilon h)=F(x(t-1)) \] is considered.
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Metastable Periodic Patterns in Singularly Perturbed Delayed Equations
Journal of Dynamics and Differential Equations, 2010The equation \[ \varepsilon\dot{x}(t)=-x(t)+f(x(t-1)) \] is considered in the limit \(\varepsilon\to 0\) for both cases of Positive Feedback (PF) and Negative Feedback (NF) by the nonlinearity \(f\), which is assumed to be odd in the positive feedback case.
Grotta-Ragazzo, C. +2 more
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Convergence in the boundary layer for singularly perturbed equations
Automatica, 1982A singularly perturbed linear finite-dimensional ordinary differential equation is considered on the half-line [0, ~). The reduced system is assumed to have a unique solution in the sense of distributions. It is proved that under reasonable conditions the solution of the full system converges to that of the reduced in the distributional sense, and the ...
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Singularly Perturbed Differential-Difference Equations
1993A delay equation $$ v\dot x\left( x \right) = - x\left( t \right) + f\left( {x\left( t \right)} \right),x\left( t \right):{R^ + } \to R, v >0, $$ (3.1) and some its generalizations have recently become a matter of interest in the theory of differential equations.
A. N. Sharkovsky +2 more
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Singularly perturbed integrodifferential equations with unstable spectrum
Ukrainian Mathematical Journal, 1989The author considers the initial value problem for the integro-ordinary differential equation \(\epsilon y'+xy+\lambda \int^{b}_{a}K(x,s)y(s)ds=f(x)\), \(x\in [a,b ...
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A survey of singularly perturbed Volterra equations
Applied Numerical Mathematics, 1997The paper contains a survey of results concerning the second kind Volterra integral equations of the form \[ \varepsilon y(t)=g(t)+ \int_0^t k(t,s,y(s))ds, \qquad 0\leq t\leq T,\tag{1} \] and the Volterra integro-differential equation of the form \[ \varepsilon y'(t)= f\Biggl( t,y(t), \int_0^t k(t,s,y(s))ds \Biggr), \quad ...
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A System of Singularly Perturbed Semilinear Equations
2009In this paper systems of singularly perturbed semilinear reaction-diffusion equations are examined. A numerical method is constructed for these systems which involves an appropriate layer-adapted piecewise-uniform mesh. The numerical approximations generated from this method are shown to be uniformly convergent with respect to the singular perturbation
J. L. Gracia +3 more
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Oscillations in Singularly Perturbed Delay Equations
1992This paper presents some recent results on the scalar singularly perturbed differentila delay equation $$[v\dot x(t) + x(t) = f(x(t - 1)).$$ (1)
A. F. Ivanov, A. N. Sharkovsky
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