Geodesic
On Carleman--Vekua Equations with Nonfinitely Supported Coefficients on a Noncompact Riemann Surface
Matematičeskie zametki, Tome 75 (2004) no. 1, pp. 3-12.

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In this paper, we study equations of the form $\partial f+Af+B\bar f=G$, on an arbitrary noncompact Riemann surface $R$, where $A$, $B$, and $G$ are given square-integrable linear differentials of genus $(0,1)$ satisfying certain additional conditions. Necessary and sufficient conditions for the solvability of the above equation are proved for the class of functions with $\Lambda_0$-behavior in the neighborhood of the ideal boundary of the surface $R$; the index of the equation is also calculated. 
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I. A. Bikchantaev. On Carleman--Vekua Equations with Nonfinitely Supported Coefficients on a Noncompact Riemann Surface. Matematičeskie zametki, Tome 75 (2004) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/MZM_2004_75_1_a0/

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