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We establish estimates (interior and up to the boundary) of solutions of the...
We use the Lyapunov vector function method and the guiding function method to obtainsufficient conditions for the existence of Poisson bounded and partially Poisson bounded solutionsof systems of differential equations.
We study a mixed problem with nonlinear dissipative boundary conditions for systems ofone-dimensional semilinear wave equations with a focusing nonlinear source that has a variablegrowth exponent. Theorems on the blow-up of solutions in finite time are proved.
We prove that a necessary and sufficient condition for the existence of a classical solutionof the inhomogeneous biharmonic equation in a bounded plane domain is the requirement ofstronger continuity of the function on the right-hand side in the equation.
We study the Tricomi problem for an advance–delay mixed type equation. Theorems onthe uniqueness and existence of a twice continuously differentiable solution are proved.
We prove the existence and uniqueness of a solution of the Darboux problem for thefourth-order Bianchi equation. The Riemann–Hadamard function is determined for the Darbouxproblem. The solution of the problem is constructed in terms of this function.
Initial value problems with various boundary conditions at the ends are studied for thebeam vibration equation taking into account the beam rotational motion under bending. Anenergy inequality is established, which implies the uniqueness of the solution of the fourinitial–boundary value problems...
We prove the existence and uniqueness of the solution of the Cauchy problem for anintegro-differential equation related to the peridynamic model in mechanics of solids.
For an integro-differential equation of the convolution type with a power nonlinearity anda variable coefficient defined on the half-line...
The connections between stochastic differential equations in which continuous anddiscontinuous random processes serve as sources of randomness and deterministic equations forthe probabilistic characteristics of solutions of these stochastic equations are studied. In the study,we use various...
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