Information on the thesis

The dissertation is devoted to investigation of solvability of the problems with
local two-point in time conditions which contain differential polynomials, for partial
differential equations in the spaces of entire functions.
The kernel of the problem for partial differential equation of second order in
time variable in which local two-point conditions are given and generally infinite
order in spatial variables is investigated. Sufficient conditions of existence of the
nontrivial solutions in the classes of entire functions, and also necessary and sufficient
conditions of existence of nontrivial quasipolynomial solutions are established. The
differential-symbol method of constructing the solutions is proposed. The conditions
of existence only trivial solution of the problem are found.
The conditions of existence and uniqueness of the solution of the problem for
homogeneous partial differential equation of second order in time and generally
infinite order in spatial variables with nonhomogeneous local two-point conditions,
and also the problem for nonhomogeneous partial differential equation of second
order in time and generally infinite order in spatial variables with homogeneous local
two-point conditions in the classes of entire functions, continuously differentiable
functions and in classes of quasipolynomials are established. The differential-symbol
method of constructing the solutions of the problem is proposed.
The problem with local two-point conditions for partial differential equation of
second order in time variable and generally infinite order in spatial variables when
the characteristic determinant of the problem identically equals to zero is investi-
gated by differential-symbol method. The conditions of existence and nonexistence
solution of the problem are found. In the case of existence of solutions of the problem
the method of their construction is proposed.
Key words: differential-symbol method, partial differential equation of infinite
order, local two-point conditions, characteristic determinant.