Massalitina Y. One-dimensional and many-dimensional integrated inequalities for continuous and discontinuous functions and their application

Dissertation work is devoted to obtaining of estimations for discontinuous functions satisfying to one-dimensional and many-dimensional, linear and nonlinear integrated inequalities. At a determination of estimations for functions of two variables, which have external saltuses of various character on some given curves, were used the theory of a measure and integral of the Lebesgue–Stieltjes. This approach has allowed to unite in final result of two cases: measure of the Lebesgue–Stieltjes, which is concentrated a curve, a) is discrete, b) is absolutely continuous. The estimations for sectionally continuous function of one variable, which satisfies to an integrated and functional Perova inequality, are obtaine. The estimations for discontinuous functions of two variables, which satisfy to inequalities, such as Vendorf, Perova, Bihari, Akinyele Olusola and have external saltuses of various character on some given curves are obtaine too. The possibility of use of the obtained estimations in the theory ofthe equations of a hyperbolic type - by reviewing a problem of the Goursat with the data on characteristics for function, which on the given curves receives impulse actions, in the qualitative theory of systems of the differential equations with impulse actions is shown.