On Global Classical Solutions of Hyperbolic Differential-Difference Equations

Abstract

© 2020, Pleiades Publishing, Ltd. Abstract: A one-parameter family of global solutions of a two-dimensional hyperbolic differential-difference equation with an operator acting with respect to a space variable is constructed. A theorem is proved stating that the resulting solutions are classical for all parameter values if the symbol of the difference operator of the equation has a positive real part. Classes of equations for which this condition is satisfied are given.