相关论文: Sharp uniqueness conditions for one-dimensional, a…

The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our…

The purpose of this paper is to prove the uniqueness theorem of solutions of eigenvalue equations on one end of Riemannian manifolds for drift Laplacians, including the standard Laplacian as a special case; we shall impose "a sort of…

We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…

We identify many new solvable subcases of the general dynamical system characterized by two autonomous first-order ordinary differential equations with purely quadratic right-hand sides; the solvable character of these dynamical systems…

Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…

In this paper we study uniqueness properties of solutions to the Zakharov-Kuznetsov equation of plasma physic. Given two sufficiently regular solutions $u_1, u_2,$ we prove that, if $u_1-u_2$ decays fast enough at two distinct times, then…

When a system of first order linear ordinary differential equations has eigenvalues of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The cost of representing…

In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the…

We give a series of very general sufficient conditions in order to ensure the uniqueness of large solutions for --$\Delta$u + f (x, u) = 0 in a bounded domain $\Omega$ where f : $\Omega$ x R $\rightarrow$ R + is a continuous function, such…

For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…

In this paper, we give the existence and uniqueness of the strong solution of one dimensional linear parabolic equation with mixed boundary conditions. The boundary conditions can be any kind of mixed Dirichlet, Neumann and Robin boundary…

In this paper, the existence and uniqueness of strong solutions to distribution dependent neutral SFDEs are proved. We give the conditions such that the order preservation of these equations holds. Moreover, we show these conditions are…

The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the…

We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of…

In this paper, we consider a nonlinear Fuchsian type partial differential equation of the second order in the complex domain. Under a very weak assumption, we show the uniqueness of the solution. The result is applied to the problem of…

In this paper we use the comparison method for investigation of first order polynomial differential equations. We prove two comparison criteria for these equations. The proved criteria we use to obtain some global solvability criteria for…

Dynamical systems with prescribed-time convergence sometimes feature a right-hand side exhibiting a singularity at the prescribed convergence time instant. In an open neighborhood of this singularity, classical absolutely continuous…

We present some interior regularity criteria of the 3-D Navier-Stokes equations involving two components of the velocity. These results in particular imply that if the solution is singular at one point, then at least two components of the…

In this article we find the equivalent conditions to assure the existence and uniqueness of positive solutions to semilinear elliptic equations wih double power nonlinearities. As a bonus, we give a simpler proof of our former result that…

In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final values of the state are considered. We investigate…