On the differential equation 𝑢ₓₓ+𝑢_{𝑦𝑦}+𝑁(𝑥)𝑢=0

On the differential equation $u_ {xx}+u_ {yy}+N(x)u=0$
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Trans. Amer. Math. Soc. 65 (1949), 259-278

DOI: https://doi.org/10.1090/S0002-9947-1949-0029055-8

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References

Zur Theorie der Funktionen, die eine lineare partielle Differentialgleichung befriedigen

Stefan Bergman, Linear operators in the theory of partial differential equations, Trans. Amer. Math. Soc. 53 (1943), 130–155. MR 7555, DOI 10.1090/S0002-9947-1943-0007555-9
Stefan Bergman, The determination of some properties of a function satisfying a partial differential equation from its series development, Bull. Amer. Math. Soc. 50 (1944), 535–546. MR 10327, DOI 10.1090/S0002-9904-1944-08183-4
Stefan Bergman, Certain classes of analytic functions of two real variables and their properties, Trans. Amer. Math. Soc. 57 (1945), 299–331. MR 12370, DOI 10.1090/S0002-9947-1945-0012370-8
Stefan Bergman, Functions satisfying certain partial differential equations of elliptic type and their representation, Duke Math. J. 14 (1947), 349–366. MR 22262
Stefan Bergman, Two-dimensional subsonic flows of a compressible fluid and their singularities, Trans. Amer. Math. Soc. 62 (1947), 452–498. MR 26498, DOI 10.1090/S0002-9947-1947-0026498-1
Josephine Mitchell, Some properties of solutions of partial differential equations given by their series development, Duke Math. J. 13 (1946), 87–104. MR 16874
Martin Eichler, Allgemeine Integration linearer partieller Differentialgleichungen von elliptischem Typ bei zwei Grundvariablen, Abh. Math. Sem. Univ. Hamburg 15 (1947), 179–210 (German). MR 29054
Stefan Bergman, Classes of solutions of linear partial differential equations in three variables, Duke Math. J. 13 (1946), 419–458. MR 18323