Sobolev periodic solutions of a partial differential equation with coefficients which depend on a parameter

V. S. Il'kiv, I. Ya. Savka, M. M. Symotyuk


The conditions of existence and uniqueness of Sobolev periodic solution for linear partial differential equation with constant complex coefficients, which depends on one real parameter, are established. It is shown that these conditions fulfill for almost all (with respect to the Lebesgue measure) parameter values.


differential equation, periodic solution, small denominator, diophantine approximation, metric estimation

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