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Resurgent analysis in several variables. II: Applications. (English) Zbl 0847.35019
Lumer, Günter (ed.) et al., Partial differential equations. Models in physics and biology. Contributions to the conference, held in Han-sur-Lesse, Belgium, in December 1993. Berlin: Akademie Verlag. Math. Res. 82, 378-400 (1994).
[For part I see ibid. 82, 351-377 (1994; Zbl 0831.35021).]
This second part contains applications of the general theory developed in the first part. More precisely, a construction of asymptotic solutions at infinity of PDE with polynomial coefficients is given. Here one needs general exponential functions of arbitrary order which involves modifications in the theory constructed in Part I. In the case of two simple examples (Helmholtz equation and Schrödinger equation for the harmonic oscillator) the mentioned asymptotic solutions are completely calculated.
For the entire collection see [Zbl 0809.00019].

35B40 Asymptotic behavior of solutions to PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J10 Schrödinger operator, Schrödinger equation
35C15 Integral representations of solutions to PDEs