For citation:
Burlutskaya M. S. A Mixed Problem for a System of First Order Differential Equations with Continuous Potential. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 2, pp. 145-151. DOI: 10.18500/1816-9791-2016-16-2-145-151, EDN: WCNQHT
A Mixed Problem for a System of First Order Differential Equations with Continuous Potential
We study a mixed problem for a first order differential system with two independent variables and continuous potential when the initial condition is an arbitrary square summable vector-valued function. The corresponding spectral problem is the Dirac system. It sets the convergence almost everywhere of a formal decision, obtained by the Fourier method. It is shown that the sum of a formal decision is a generalized solution of a mixed problem, understood as the limit of classical solutions for the case of smooth approximation of the initial data of the problem.
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