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On the Cauchy problem in classes of resurgent functions. (English. Russian original) Zbl 0793.35019
Sov. Math., Dokl. 44, No. 2, 496-500 (1992); translation from Dokl. Akad. Nauk SSSR 320, No. 3, 551-555 (1991).
From the paper: We consider the Cauchy problem for differential equations of the form $-k^{m-1} {\partial \psi \over \partial t}+H \left( x,- {\partial \over \partial x},k \right) \psi=0,\quad \psi |_{t=0}=\psi_ 0(x).$ Here $$k$$ is a parameter, and $$H(x,p,k)$$ is a polynomial in $$(p,k)$$ of degree $$m$$ with coefficients holomorphic in $$x$$. Following the idea of Balian and Bloch, we seek solutions to this type of equation in the class of resurgent functions.
##### MSC:
 35G25 Initial value problems for nonlinear higher-order PDEs 35A20 Analyticity in context of PDEs 35C15 Integral representations of solutions to PDEs 35A30 Geometric theory, characteristics, transformations in context of PDEs
##### Keywords:
resurgent functions; canonical Maslov operator