zbMATH — the first resource for mathematics

Asymptotic solutions of differential equations when the motion of the Hamilton field is finite. (English. Russian original) Zbl 0647.34055
Differ. Equations 23, No. 2, 220-227 (1987); translation from Differ. Uravn. 23, No. 2, 300-308 (1987).
Consider a differential equation of the form: \(H(x,\hat p,k)u=f(x)\), where \[ \hat p=-i\frac{d}{dx},\;H(x,p,k)=\sum^{m}_{j=0}(p^ j+ \sum^{j-1}_{s=0} a_ s(x)k^{j-s}p^ s) \] and f is a regular function. A construction method of asymptotic solutions is proposed.
Reviewer: C.Simirad
34E05 Asymptotic expansions of solutions to ordinary differential equations
47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
47J25 Iterative procedures involving nonlinear operators