Solution Of General Boundary Value Problem Research Articles

Solvability of general boundary-value problems in a half-space for inhomogeneous differential equations with constant coefficients

We present sufficient conditions for the existence of solutions of general boundary-value problems in a half-space for inhomogeneous differential equations with constant coefficients and arbitrary boundary data in the space of tempered distributions.

Limit theorems for one-dimensional boundary-value problems

We study the limit with respect to a parameter in the uniform norm for the solutions of general boundary-value problems for systems of linear ordinary differential equations of the first order. A generalization of the Kiguradze theorem (1987) to this class of problems is obtained. The conditions imposed on the asymptotic behavior of the coefficients of systems are weakened as much as possible. Sufficient conditions for the uniform convergence of Green matrices to the Green matrix of the limit boundary-value problem are also established.

DIFFERENTIAL PROPERTIES OF SOLUTIONS OF ELLIPTIC BOUNDARY-VALUE PROBLEMS WITH POWER SINGULARITIES ON THE RIGHT-HAND SIDES

Exact bounds are obtained for the derivatives of the solutions of general boundary-value problems for elliptic equations of order 2m in the neighborhood of a power singularity. The order of the singularity is arbitrary, and it can be at an interior point or on the boundary.