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In this article we define the Coulomb energy space and study its fundamental properties as a function space. [ABSTRACT FROM AUTHOR]

We study the Cauchy problem for the Schrödinger equation with a mixed type nonlinear term. We analyze the local and global properties of solutions in dependence of the nonlinear power, the repulsive or attractive character of nonlinear interaction and the size of the initial data. [ABSTRACT FROM AUTHOR]

Due to the unprecedented COVID-19 pandemic, and the resultant recommendations of the public health officials and local governments, the Organizing committee decided to use remote technologies to hold the AMEE'20 conference as a virtual meeting in place of the usual in-person conference. The present volume of proceedings consists of the papers presented during the 46 th International Conference "Applications of Mathematics in Engineering and Economics" (AMEE'20), 7- 13 June 2020. The Conference is organized every year by the Faculty of Applied Mathematics and Informatics at the Technical University of Sofia and the Faculty of Mathematics and Informatics at Sofia University "St. Kliment Ohridski". [Extracted from the article]