Existence and smoothness of solutions of a singular differential equation of hyperbolic type

Abstract

This paper investigates the question of the existence of solutions to the semiperiodic Dirichlet problem for a class of singular differential equations of hyperbolic type. The problem of smoothness of solutions is also considered, i.e., maximum regularity of solutions. Such a problem will be interesting when the coefficients are strongly growing functions at infinity. For the first time, a weighted coercive estimate was obtained for solutions to a differential equation of hyperbolic type with strongly growing coefficients.

Keywords

• resolvent
• hyperbolic type equation
• maximal regularity
• unbounded domain