Existence of solutions for nonlinear impulsive differential equations with Dirichlet boundary conditions

In this paper, we consider the existence of solutions for a class of nonlinear impulsive problems with Dirichlet boundary conditions. We obtain some new existence theorems of solutions for the nonlinear impulsive problem by using critical point theory. We extend and improve some recent results.     

Multiple Solutions of Nonlinear Impulsive Differential Equations with Dirichlet Boundary Conditions via Variational Method

In this paper, we consider the existence of multiple solutions for second-order nonlinear impulsive differential equations with Dirichlet boundary condition. We obtain some existence theorems of solutions for the nonlinear problem when the impulsive functions satisfies the superlinear growth conditions by critical point theory. We extend and improve some recent results.     

Variational Approach to Fourth-Order Impulsive Differential Equations with Two Control Parameters

In this paper, we are concerned with the multiplicity of solutions for a fourth-order impulsive differential equation with Dirichlet boundary conditions and two control parameters. Using variational methods and a three critical points theorem, we give some new criteria to guarantee that the impulsive problem has at least three classical solutions. We also provide an example in order to illustrate the main abstract results of this paper.     

Existence of solutions for a damped nonlinear impulsive problem with Dirichlet boundary conditions

In this paper, we consider the existence of solutions for second‐order nonlinear damped impulsive differential equations with Dirichlet boundary condition. By critical point theory, we obtain some existence theorems of solutions for the nonlinear problem. We extend and improve some recent results. Copyright © 2013 John Wiley & Sons, Ltd.     

Multiple solutions of boundary‐value problems for impulsive differential equations

In this paper, we investigate the existence of multiple solutions to a second‐order Dirichlet boundary‐value problem with impulsive effects. The proof is based on critical point theorems. Copyright © 2011 John Wiley & Sons, Ltd.     

Existence of solutions for impulsive Dirichlet problems with the parameter inequality reverse

In this paper, we consider the existence and multiplicity for second‐order nonlinear impulsive differential equations with Dirichlet boundary condition and a parameter. By using critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one solution or infinitely many solutions, assuming that the impulsive functions satisfy the superlinear growth condition and the parameter inequality is reverse. Our results extend and improve some recent results. Copyright © 2013 John Wiley & Sons, Ltd.     

Impulsive boundary value problems for p(t)-Laplacian’s via critical point theory

In this paper we investigate the existence of solutions to impulsive problems with a p(t)-Laplacian and Dirichlet boundary value conditions. We introduce two types of solutions, namely a weak and a classical one which coincide because of the fundamental lemma of the calculus of variations. Firstly we investigate the existence of solution to the linear problem, i.e. a problem with a fixed rigth hand side. Then we use a direct variational method and next a mountain pass approach in order to get the existence of at least one weak solution to the nonlinear problem.     

Variational approach to some damped Dirichlet problems with impulses

In this paper, we study the existence of solutions for damped nonlinear impulsive differential equations with Dirichlet boundary conditions. By using critical point theory and variational methods, we give some new criteria to guarantee that the impulsive problems have at least one solution. Some recent results are extended and significantly improved. Finally, some examples are presented to illustrate our main results. Copyright © 2013 John Wiley & Sons, Ltd.     

Infinitely many solutions of a second-order <Emphasis Type="Italic">p</Emphasis>-Laplacian problem with impulsive condition

Using the critical point theory and the method of lower and upper solutions, we present a new approach to obtain the existence of solutions to a p-Laplacian impulsive problem. As applications, we get unbounded sequences of solutions and sequences of arbitrarily small positive solutions of the p-Laplacian impulsive problem.     

一类自然增长的拟线性椭圆型方程的非平凡解

本文利用不光滑泛函的临界点理论证明了与泛函 I(u)=∫_Ω[1/2a_(ij)(x,u)D_iuD_ju-G(x,u)]dx,G(x,u)=∫_0g(x,t)dt相对应的Euler-Lagrange方程齐次Dirichlet问题非平凡解的存在性.证明改进了对α_(ij)(x,u)与G(x,u)所加的条件.     

Existence and multiplicity of solutions for an impulsive boundary value problem with a parameter via critical point theory

In this paper, an impulsive boundary value problem with a parameter is considered. By using critical point theory, some criteria are obtained to guarantee that the impulsive problem has at least one solution, two solutions and infinitely many solutions when the parameter lies in different intervals. The results obtained are also valid and new for a problem discussed in the literature.     

Positive solutions for a p-Laplacian type system of impulsive fractional boundary value problem

In this paper, the aim is to discuss a class of p-Laplacian type fractional Dirichlet"s boundary value problem involving impulsive impacts. Based on the approaches of variational method and the properties of fractional derivatives on the reflexive Banach spaces, the existence results of positive solutions for our equations are established. Two examples are given at the end of each main result.     

Infinitely many solutions for a p-Laplacian boundary value problem with impulsive effects

In this paper, a p-Laplacian boundary value problem with impulsive effects is considered. By using variational methods and critical point theorems, some criteria are obtained to guarantee that the impulsive problem has infinitely many solutions when the impulsive functions satisfy superlinear or sublinear conditions. Our results further improve some existing results.     

Variational methods to Sturm-Liouville boundary value problem for impulsive differential equations

In this paper, we study a linear Sturm-Liouville impulsive problem and a nonlinear Sturm-Liouville impulsive problem. By applying a new approach via critical point theory and variational methods, the existence results of positive solutions are obtained.     

Variational formulation of a damped Dirichlet impulsive problem

In this letter we introduce the concept of a weak solution for a damped linear equation with Dirichlet boundary conditions and impulses. We use the classical Lax–Milgram Theorem to reveal the variational structure of the problem and get the existence and uniqueness of weak solutions as critical points. This will allow us in the future to deal with the corresponding nonlinear problems and look for solutions as critical points of weakly lower semicontinuous functionals.     

Finite-time stabilization of nonlinear impulsive dynamical systems

Finite-time stability involves dynamical systems whose trajectories converge to a Lyapunov stable equilibrium state in finite time. For continuous-time dynamical systems finite-time convergence implies nonuniqueness of system solutions in reverse time, and hence, such systems possess non-Lipschitzian dynamics. For impulsive dynamical systems, however, it may be possible to reset the system states to an equilibrium state achieving finite-time convergence without requiring non-Lipschitzian system dynamics. In this paper, we develop sufficient conditions for finite-time stability of impulsive dynamical systems using both scalar and vector Lyapunov functions. Furthermore, we design hybrid finite-time stabilizing controllers for impulsive dynamical systems that are robust against full modelling uncertainty. Finally, we present a numerical example for finite-time stabilization of large-scale impulsive dynamical systems.     

一类脉冲中立型抛物系统振动性

考虑一类具高阶Laplace算子的脉冲中立型抛物偏微分系统的振动性,借助于一阶脉冲时滞微分不等式,得到了该类系统在Dirichlet边值条件下所有解振动的若干充分条件.所得结果充分反映了脉冲和时滞在系统振动中的影响作用.