On one method of solving singularly perturbed systems of Tikhonov's type (Q1795324)

The paper deals with a holomorphic regularization for a singularly perturbed system \[ \frac{dy}{dt}=f(t,y,v),\;\varepsilon \frac{dv}{dt}=F(t,y,v),\;t\in[0,T],\;y\in\mathbb{R}^k, \;v\in\mathbb{R}, \] \[ y(0,\varepsilon)=y^0, \;v(0,\varepsilon)=v_0, \] where it is assumed that the functions \(f\) and \(F\) are holomorphic in certain closed domain of the space of real variables \((t,y,v)\) containing an initial point \((0,y^0,v_0).\) Rewriting the solution into the form of series of integrals it was shown that under conditions of the Tikhonov theorem, the solution \((y(t,\varepsilon),v(t,\varepsilon))\) of the initial problem is pseudo-holomorphic at the point \(\varepsilon=0\) in the global sense.