相关论文: Continuous parameter dependence for solutions of o…

We prove that an auxiliary two-point boundary value problem presented in V. L. Kharitonov, Lyapunov matrices for a class of time delay systems, Systems & Control Letters 55 (2006) 610-617 has linearly dependent boundary conditions, and…

A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…

We obtain boundary Holder gradient estimates and regularity for solutions to the linearized Monge-Ampere equations under natural assumptions on the domain, Monge-Ampere measures and boundary data. Our results are affine invariant analogues…

Using the direct method of the calculus of variations we investigate the existence, uniqueness and continuous dependence on parameters for solutions of second order discrete anisotropic equations with Dirichlet boundary conditions.

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

We develop a new theory for treating boundary problems for linear ordinary differential equations whose fundamental system may have a singularity at one of the two endpoints of the given interval. Our treatment follows an algebraic…

Dependence on the parameter is continuous when perturbations of the parameter preserves strict preference for one alternative over another. We characterise this property via a utility function over alternatives that depends continuously on…

We establish global pointwise bounds for the Green's matrix for divergence form, second order elliptic systems in a domain under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local…

This work is devoted to the study of first order linear problems with involution and general linear conditions. We first study the problem in the case of antiperiodic boundary conditions, giving an explicit Green's function for it. Then we…

A method of looking for boundary conditions consistent with the integrability property of multidimensional Kadomtsev-Petviashvili (KP) type equations is discussed. The method is based on involutions of the Lax pair taken at the border…

We study linear boundary-value problems for systems of first-order ordinary differential equations with the most general boundary conditions in the normed spaces of continuously differentiable functions on a finite closed interval. The…

Initial-boundary value problems in a half-strip with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in classes of regular solutions in the cases of…

Generalized power asymptotic expansions of solutions to differential equations that depend on parameters are investigated. The changing nature of these expansions as the parameters of the model cross critical values is discussed. An…

A system of differential equations of the Okubo normal form containing accessory parameters is considered. A condition for determining special values of the accessory parameters is given. It is shown that the special values give the…

Symmetric hyperbolic systems and constantly hyperbolic systems with constant coefficients and a boundary condition which satisfies a weakened form of the Kreiss-Sakamoto condition are considered. A well-posedness result is established which…

We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616--621] and motivated by Gordin [Soviet Math.…

We mainly investigate the continuous dependence on parameters of nontrivial solutions for a generalized poly-Laplacian system on the weighted finite graph $G=(V, E)$. We firstly present an existence result of mountain pass type nontrivial…

In this paper, we look at a linear system of ordinary differential equations as derived from the two-dimensional Ginzburg-Landau equation. In two cases, it is known that this system admits bounded solutions coming from the invariance of the…

In the paper boundary-value problem for a multidimensional system of partial differential equations with fractional derivatives in Riemann-Liouville sense with constant coefficients is studied in a rectangular domain. The existence and…

We provide non-asymptotic, relative deviation bounds for the eigenvalues of empirical covariance and Gram matrices in general settings. Unlike typical uniform bounds, which may fail to capture the behavior of smaller eigenvalues, our…