Homogeneous Problem with two-point in time Conditions for Some Equations of Mathematical Physics

Z. Nytrebych, Oksana M. Malanchuk, Volodymyr S. Il'kiv, Petro Ya. Pukach


We study the problem for homogeneous partial differential equations of two variables
of the second order with respect to the time variable in which there given homogeneous two-point
conditions, and finite order with respect to another (spatial) variable. We propose a method of
construction nontrivial solutions of the problem when the characteristic determinant of the problem
is nontrivial and the set of its zeroes is not empty. We applied this method to the construction of
non-zero solutions of homogeneous two-point problems for some equations of mathematical physics.


35G15, 35K05


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