This paper is concerned with a linear-quadratic (LQ, for short) optimal control problem backward stochastic differential equations (BSDEs, short), where the coefficients of system and weighting matrices in cost functional are allowed to be random. By variational method, optimality system, which coupled linear forward-backward equation (FBSDE, derived, by Hilbert space unique solvability obtaine...

The exact conditions sufficient for the unique solvability of initial value problem a system linear fractional functional differential equations determined by isotone operators are established. In sense, obtained optimal. method test elements intended estimation spectral radius operator is used. solution presented Neumann’s series. All theoretical investigations shown in examples. A pantograph-...

This paper is concerned with a linear quadratic optimal control problem of delayed backward stochastic differential equations. An explicit representation derived for the control, which feedback entire past history and expected value future state trajectory in short period time. To obtain feedback, new class Riccati equations delayed-advanced forward-backward are introduced. Furthermore, unique ...

Abstract The integro-differential equation of heat conduction with the time-convolution integral on right side is considered. direct problem initial-boundary for this equation. Two inverse problems are studied consisting in determining a kernel member two given additional conditions respect to solution problems, respectively. replaced equivalent system equations unknown functions and basis cont...

Considered are linear algebraic systems of equations and/or inequalities involving linear dependencies between interval-valued parameters. The goal is to characterize weak and strong solvability of such systems. Since any parametric interval equation is equivalent to a system of parametric interval inequalities, the focus is on the latter. We discuss an algorithmic procedure for characterizing ...

Sharp conditions are obtained for the unique solvability of focal boundary value problems higher-order functional differential equations under integral restrictions on operators. In terms norm operator, unimprovable problem established in explicit form. If these not fulfilled, then there exists a positive bounded operator with given such that this is uniquely solvable. symmetric case, some esti...

In this work, we used reflexive Banach spaces to study the differential variational—hemivariational inequality problems with constraints. We established a sequence of perturbed variational–hemivariational constraints and penalty coefficients. Then, for each inequality, proved unique solvability convergence solutions problems. Following that, proposed mathematical model viscoelastic rod in unila...

Tropical differential equations are introduced and an algorithm is designed which tests solvability of a system of tropical linear differential equations within the complexity polynomial in the size of the system and in its coefficients. Moreover, we show that there exists a minimal solution, and the algorithm constructs it (in case of solvability). This extends a similar complexity bound estab...