On One Type of Nonlinear Cauchy – Riemann Equation with a Singularity in the Lowest Coefficient
DOI:
https://doi.org/10.52575/2687-0959-2026-58-2-176-182Keywords:
Cauchy – Riemann Operator, Strong Isolated Singularities, Pompeiu – Vekua Integral OperatorAbstract
In this paper, one class of nonlinear equations with the Cauchy – Riemann operator is considered. Such equation is reduced to a linear equation by a substitution; conditions under which this substitution makes a one-to-one mapping are formulated. The coefficient of the equation at the unknown function has an isolated strong power sinularity at zero, and after its elimitation it is continuously differentiable in a neighborhood of zero sufficiently many times. Using the Taylor expansion of the coefficient and direct integration of the polynomial part, by means of the Pompeiu – Vekua operator an integral representation of solutions to this equation is obtained.
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