a second order boundary value problem with impulsive effects on an unbounded domain abstract we study a second order nonlinear differential equation on an unbounded domain with solutions subject to impulsive conditions and the sturm liouville type boundary conditions the existence results are obtained via applications of krasnosel ski s fixed point theorem for the sum of a completely continuous operator and a contraction

on the solvability of periodic boundary value problems with impulse in this work we obtain some new results concerning the existence of solutions to an impulsive first order nonlinear ordinary differential equation with periodic boundary conditions the ideas involve differential inequalities and schaefer s fixed point theorem

existence results for abstract impulsive second order neutral functional differential equations abstract we establish the existence of mild solutions for a class of impulsive second order partial neutral functional differential equations with infinite delay in a banach space

exact results for a checkerboard ising model with crossing and four spin interactions a seven parameter ising model with crossing and four spin interactions on a checkerboard lattice is mapped by a duality transformation onto a general eight vertex model which has only five independent parameters in a six dimensional subspace of the ising model for which the corresponding eight vertex model satisfies the free fermion condition an exact solution is found

stabilization of solutions of a degenerate nonlinear diffusion problem i 4 u f u in l l x r u tl t o in r u x 0 uo x in l l where m 1 is a parameter f is locally lipschitz continuous f 0 0 and u is bounded problems of this form arise in a number of areas of science for instance in models for gas or fluid flow in porous media 2 and for the spread of certain biological populations 13 161 this paper is divided into two parts in part i we consider what may be called the motivating example problem i which consists of problem i with the special choice f u u 1 u u a 1 for suitably restricted parameters a we begin by describing in detail the set l of nonnegative equilibrium solutions of problem i clearly 8 l contains the trivial solution u 0 for all l 0 write 8 l e l o in the description of z l there are two critical parameter values lo and l1 with 0 lo l1 j we show that i g l 4 for 0 l lo

existence of positive solutions for sturm liouville boundary value problems on the half line in this paper we establish sufficient conditions to guarantee the existence of at least one positive solution a unique positive solution and multiple positive solutions for the sturm liouville boundary value problem on the half line by using an effective operator the fixed point theorems in cone especially krasnoselskii fixed point theorem can be applied to such systems and then existence criteria are established the interesting point of the results is that the nonlinear term f can be sign changing

duality transformations for spin 1 2 lattice systems by using a procedure introduced in the previous work the author considers duality transformations for spin 1 2 lattice systems the author shows that in some cases given a self dual model a new self dual model can be obtained from it several examples of this fact are given in particular the author analyses a system consisting of two interacting baxter wu models which present close analogies with the ashkin teller model

calculus of variations for a boundary value problem of differential system on the half line boundary value problem of second order differential equations on the half line is investigated in this paper the method mainly depends on the calculus of variations to the classical functionals sufficient conditions are obtained for the existence of the solutions

existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti periodic boundary conditions this paper describes the method of quasilinearization for first order nonlinear impulsive functional differential equations with anti periodic boundary conditions a monotone iterative technique coupled with lower and upper solutions is employed to obtain sequences of approximate solutions converging monotonically and quadratically to the unique solution of the problem at hand 2007 elsevier ltd all rights reserved

nonlinear boundary value problem of first order impulsive functional differential equations this paper discusses nonlinear boundary value problem for first order impulsive functional differential equations we establish several existence results by using the lower and upper solutions and monotone iterative techniques two examples are discussed to illustrate the efficiency of the obtained results

three 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 multiplicity of solutions is obtained by three critical points theorem an example is presented to illustrate main result

periodic solutions for ordinary differential equations with sublinear impulsive effects abstract the continuation method of topological degree is used to investigate the existence of periodic solutions for ordinary differential equations with sublinear impulsive effects the applications of the abstract approach include the generalizations of some classical nonresonance theorem for impulsive equations for instance the existence theorem for asymptotically positively homogeneous differential systems and the existence theorem for second order equations with landesman lazer conditions

spin 1 2 lattice systems a new approach to duality transformations a straightforward algebraic technique is introduced in order to establish duality relations between spin 1 2 lattice systems a new self duality relation is found

multiplicity results for sturm liouville boundary value problems multiplicity results for sturm liouville boundary value problems are obtained proofs are based on variational methods

the multiplicity of solutions for perturbed second order hamiltonian systems with impulsive effects abstract in this paper we study the existence of multiple solutions for a class of second order impulsive hamiltonian systems we give some new criteria for guaranteeing that the impulsive hamiltonian systems with a perturbed term have at least three solutions by using a variational method and some critical points theorems of b ricceri we extend and improve on some recent results finally some examples are presented to illustrate our main results

an application of variational method to second order impulsive differential equation on the half line abstract in this paper we study the multiplicity of solutions for second order impulsive differential equation with a parameter on the half line by using a variational method and a three critical points theorem we give some new criteria to guarantee that the impulsive problem has at least three classical solutions also an example is given in this paper to illustrate the main results

new comparison results for impulsive integro differential equations and applications we prove some new maximum principles for ordinary integro differential equations this allows us to introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear first order impulsive integro differential equation

the existence and multiplicity of solutions for an impulsive differential equation with two parameters via a variational method abstract in this paper we study the existence and multiplicity of classical solutions for a second order impulsive differential equation with periodic boundary conditions by using a variational method and critical point theory we give some new criteria to guarantee that the impulsive problem has at least one solution two solutions and infinitely many solutions when the parameter pair c lies in different intervals respectively some examples are given in this paper to illustrate the main results

impulsive periodic boundary value problems of first order differential equations in this paper by using schaeffer s theorem we prove new existence theorems for a nonlinear periodic boundary value problem of first order differential equations with impulses our results improve and generalize some known results

robust filtering for a class of stochastic uncertain nonlinear time delay systems via exponential state estimation we investigate the robust filter design problem for a class of nonlinear time delay stochastic systems the system under study involves stochastics unknown state time delay parameter uncertainties and unknown nonlinear disturbances which are all often encountered in practice and the sources of instability the aim of this problem is to design a linear delayless uncertainty independent state estimator such that for all admissible uncertainties as well as nonlinear disturbances the dynamics of the estimation error is stochastically exponentially stable in the mean square independent of the time delay sufficient conditions are proposed to guarantee the existence of desired robust exponential filters which are derived in terms of the solutions to algebraic riccati inequalities the developed theory is illustrated by numerical simulation