Gamma-lines approach in the study of global behaviour of solutions of complex differential equations

Abstract

This article has two novel aspects in complex differential equations: it starts the studies of the global behaviour of solutions in arbitrary domains and also the studies of gamma-lines of the solutions. This is done for solutions of some classes of equations involving the basic Schrödinger type equations, also those with entire coefficients, which we consider in ‘almost’ arbitrary domains. In particular case, when the domain is the complex plane, we study deficiency of gamma-lines of solutions of algebraic Schrödinger equations and prove that the deficiency is equal to zero for any curve which does not pass through zero.