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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.