相关论文: On bounded solutions for second order linear diffe…

A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…

This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…

The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…

This brief gives a set of unified Lyapunov stability conditions to guarantee the predefined-time/finite-time stability of a dynamical systems. The derived Lyapunov theorem for autonomous systems establishes equivalence with existing…

We obtain local boundedness of weak solutions of double phase quasilinear parabolic equations of the form \[u_t-\text{div} \left(|\nabla u|^{p-2}\nabla u+a(x,t)|\nabla u|^{q-2}\nabla u\right)=0,\] where, we have imposed the restrictions…

We propose the existence theorem for bounded solutions to the system of 2-nd order ODE. Dynamical applications have been considered.

This paper is concerned with boundary stabilization of two-dimensional hyperbolic systems of partial differential equations. By adapting the Lyapunov function previously proposed by the second author for linearized hyperbolic systems with…

In this paper, we consider a linear fractional differential equation with fractional boundary conditions. First, by obtaining Green's function, we derive the Lyapunov-type inequalities for such boundary value problems. Furthermore, we use…

The detailed construction of the general solution of a second order non-homogenous linear operatordifference equation is presented. The wide applicability of such an equation as well as the usefulness of its resolutive formula is shown by…

This paper is devoted to provide some new results on Lyapunov type inequalities for the periodic boundary value problem at higher eigenvalues. Our main result is derived from a detailed analysis on the number and distribution of zeros of…

We establish local boundedness for solutions to fractional porous medium-type equations in the fast diffusion regime, under optimal tail assumptions.

In this article we study solutions to second order linear difference equations with variable coefficients. Under mild conditions we provide closed form solutions using finite continued fraction representations. The proof of the results are…

We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…

We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…

For the $\mathfrak{so}(4)$ free rigid body the stability problem for the isolated equilibria has been completely solved using Lie-theoretical and topological arguments. For each case of nonlinear stability previously found we construct a…

In this paper, we consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…

A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…

This technical note studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibit predefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-time stable and an upper bound of…

We present a methodology for establishing the existence of quadratic Lyapunov inequalities for a wide range of first-order methods used to solve convex optimization problems. In particular, we consider i) classes of optimization problems of…

We deal with the existence of solutions having L2 regularity for a class of non autonomous evolution equations. Associated with the equation, a general non local condition is studied. The technique we used combines a finite dimensional…