1 - 10 of 16 articles
We find extremal solutions of a two-point sixth-order boundary value problem.
We consider the properties of the positiveness, fractional power, boundedness, and separation of the singular Sturm-Liouville operator in a weighted space depending on the behavior of its coefficients. We derive necessary and sufficient conditions for its positiveness, trace class property,...
For a fractional ordinary differential equation with the Dzhrbashyan-Nersesyan operator, we prove a theorem on the existence and uniqueness of a solution of a boundary value problem with shift.
We obtain sufficient conditions for the existence of at least one absolutely continuous solution of a nonlinear functional-differential inclusion in a finite-dimensional space with nonlinear set-valued functional boundary conditions. The set-valuedness of the dynamics may be due to the presence...
We construct and justify the asymptotics of the solution of a boundary value problem for a singularly perturbed system of two second-order ordinary differential equations that contain distinct powers of a small parameter multiplying second-order derivatives for the case of a multiple root of the...
We prove an existence theorem for weak solutions of stochastic differential equations with standard and fractional Brownian motions and with discontinuous coefficients. A weak solution of an equation is understood as a weak solution of a stochastic differential inclusion constructed on the basis...
For the equation y
2−1) = 0, we suggest an analytic construction of kinklike solutions (solutions bounded on the entire line and having finitely many zeros) in the form of rapidly convergent series in products of exponential and trigonometric functions. We show that, to within sign and...
In a Hilbert space H, we study the Fredholm property of a boundary value problem for a fourth-order differential-operator equation of elliptic type with unbounded operators in the boundary conditions. We find sufficient conditions on the operators in the boundary conditions for the problem to be...
For the solutions of an elliptic equation with constant coefficients, we prove uniqueness theorems that generalize the classical boundary uniqueness theorems for analytic functions.
For a hyperbolic equation of a form earlier unstudied, we consider two problems with normal derivatives in the boundary conditions. For each of these problems, we prove the existence of a unique reduction to the Goursat problem.
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