Solutions to the operator equation \(i\varepsilon dy/dt=A(t)y\) on intervals containing turning points. (English. Russian original) Zbl 0964.34039

Theor. Math. Phys. 122, No. 3, 298-311 (2000); translation from Teor. Mat. Fiz. 122, No. 3, 357-371 (2000).
The author studies the asymptotic behavior as \(\varepsilon \rightarrow 0\) of the solution to the equation \[ i \varepsilon \frac{dy}{dt} =A(t)y , \] where \(A(t)\) is a linear closed operator defined on a dense subset of a Banach space \(X\). The solutions to the above equation are constructed as formal asymptotic expansions as \(\varepsilon \rightarrow 0\) on intervals containing parabolic or hyperbolic turning points. A recursive scheme for finding the succesive terms of these expansions are obtained.


34D05 Asymptotic properties of solutions to ordinary differential equations
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
34G10 Linear differential equations in abstract spaces
34E05 Asymptotic expansions of solutions to ordinary differential equations
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