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Contrast structure of step type for an initial value problem. (Russian. English summary) Zbl 0902.34043

Consider the singularly perturbed system \[ \varepsilon dx/dt =-x[x-f(y,t)],\qquad dy/dt = F(x,y,t), \] where \(\varepsilon >0\) is a small parameter, with the initial conditions \( x (0,\varepsilon) = x^0 >0\), \(y(0,\varepsilon) = y^0\). Under the assumption that the associated system \[ dx/d\tau =-x[x-f(y,t)] \] has intersecting families of equilibria (this formulation is due to the reviewer), the author proves a theorem on the existence of an interior layer of step type.

MSC:

34D15 Singular perturbations of ordinary differential equations
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
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