Generalized solutions for linear operators with weakened a priori inequalities

• Date: 2010
• Main Authors: Anikushyn, A. V., Nomirovs'kii, D. A., Анікушин, А. В., Номіровський, Д. А.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2933
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We propose an approach to the investigation of generalized solutions of linear operators that satisfy weakened a priori inequalities. This approach generalizes several well-known definitions of generalized solutions of operator equations. We prove existence and uniqueness theorems for a generalized...