Abstract
The paper is concerned with the differential equation\(V_{\bar z} = C(z,\bar z)\bar V\) with\(m^2 (\log C)_{z\bar z} + + \varepsilon C\bar C = 0,m > 0,\varepsilon = \pm 1\). The Vekua resolvents are determined by means of an associated second-order differential equation. Applications are given to pseudo-analytic functions, to a differential equation in the theory of several complex variables and to the Ernst equation in general relativity.
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