To the theory of semi-linear equations in the plane

• Published in: Український математичний вісник
• Date: 2019
• Main Authors: Gutlyanskii, V.Ya., Nesmelova, O.V., Ryazanov, V.I.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2019
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/169434
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: To the theory of semi-linear equations in the plane / V.Ya. Gutlyanskii, O.V. Nesmelova, V.I. Ryazanov // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 105-140. — Бібліогр.: 74 назв. — англ.

In two dimensions, we present a new approach to the study of the semilinear equations of the form div[A(z)∇u] = f(u), the diffusion term of which is the divergence uniform elliptic operator with measurable matrix functions A(z),whereas its reaction term f(u) is a continuous non-linear function. Assu...