Semilinear equations in a plane and quasiconformal mappings
DOI:
https://doi.org/10.15407/dopovidi2017.01.010Keywords:
Beltrami equation, Bieberbach equation, Keller– Osserman condition, quasiconformal mappings, semilinear elliptic equationsAbstract
We consider generalizations of the Bieberbach equation with nonlinear right parts, which makes it possible to study many problems of mathematical physics in inhomogeneous and anisotropic media with smooth characteristics. We establish interconnections of these semilinear equations with quasiconformal mappings, obtain on this basis, a series of theorems on the existence of their solutions that blow-up on the boundary of a unit disk, as well as on punctured unit disks and rings, and give their explicit representations.
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