Functional differential equations with non-local boundary conditions.
Functional differential inequalities with unbounded delay
Classical solutions of functional partial differential inequalities with initial boundary conditions are estimated by maximal solutions of suitable problems for ordinary functional differential equations. Uniqueness of solutions and continuous dependence on given functions are obtained as applications of the comparison result. A theorem on weak functional differential inequalities generated by mixed problems is proved. Our method is based on an axiomatic approach to equations with unbounded delay....
Functions with derivatives in spaces of Morrey type and elliptic equations in unbounded domains
We introduce a sort of "local" Morrey spaces and show an existence and uniqueness theorem for the Dirichlet problem in unbounded domains for linear second order elliptic partial differential equations with principal coefficients "close" to functions having derivatives in such spaces.
Fundamental inequalities on firmly stratified sets and some applications.
Fundamental operator-valued functions of singular differential operators in Banach spaces.
Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition
The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective...