POSITIVE SOLUTIONS TO A NONHOMOGENEOUS NONAUTONOMOUS SECONDORDER BOUNDARY VALUE PROBLEM

The existence of multiple positive solutions is studied for a nonlinear nonautonomous second-order boundary value problem with nonhomogeneous boundary conditions. In order to describe the growth behaviors of nonlinearity on some bounded sets, two height functions are introduced. By considering the integrals of the height functions and applying the Krasnosel'skii fixed point theorems on a cone, several new results are proved.     

平衡问题变分包含问题及不动点问题的二次极小化

借助预解式技巧,寻求二次极小化问题minx∈Ω‖x‖2的解,其中Ω是Hilbert空间中某一广义平衡问题的解集,与一无穷族非扩张映像的公共不动点的集合,以及某一变分包含的解集的交集．在适当的条件下,逼近上述极小化问题的解的一新的强收敛定理被证明．     

A new hybrid method for solving a generalized equilibrium problem, solving a variational inequality problem and obtaining common fixed points in Banach spaces, with applications

The purpose of this paper is to prove by using a new hybrid method a strong convergence theorem for finding a common element of the set of solutions for a generalized equilibrium problem, the set of solutions for a variational inequality problem and the set of common fixed points for a pair of relatively nonexpansive mappings in a Banach space. As applications, we utilize our results to obtain some new results for finding a solution of an equilibrium problem, a fixed point problem and a common zero-point problem for maximal monotone mappings in Banach spaces.     

THE GROWTH OF SOLUTIONS OF SYSTEMS OF COMPLEX NONLINEAR ALGEBRAIC DIFFERENTIAL EQUATIONS

We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.     

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.     

一类复差分方程组的解的增长级（英文）

In this paper, using Nevanlinna theory of the value distribution of meromorphic functions, the problem of growth order of solutions of a class of system of complex difference equations is investigated, some results are improved and generalized. More precisely,some results of the growth order of solutions of system of differential equations to difference equations are extended.     

The Existence and Multiplicity of Solutions for Second-order Impulsive Differential Equations on the Half-line

In this paper, we consider the existence and multiplicity of solutions for a class of nonlinear impulsive problem on the half-line. By using a variational method and a variant fountain theorem, we obtain some new criteria to guarantee that the impulsive problem has at least one solution and infinitely many solutions respectively. We extend and improve some recent results.     

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.     

Boundedness and Nonemptiness of the Efficient Solution Sets in Multiobjective Optimization

For a given multiobjective optimization problem, we study recession properties of the sets of efficient solutions and properly efficient solutions. We work out various consequences based on the obtained recession properties, including a characterization for the boundedness and nonemptiness of the set of (properly) efficient solutions when the problem is a convex problem. We also show that the boundedness and nonemptiness of the set of efficient solutions is equivalent to that of the set of properly efficient solutions under an additional mild condition. Finally, we provide some new verifiable necessary conditions for the nonemptiness of the set of efficient solutions in terms of the associated recession functions and recession cones.     

A brain storm optimization approach for the cumulative capacitated vehicle routing problem

The cumulative capacitated vehicle routing problem (CCVRP) is a combinatorial optimization problem which aims to minimize the sum of arrival times at customers. This paper presents a brain storm optimization algorithm to solve the CCVRP. Based on the characteristics of the CCVRP, we design new convergent and divergent operations. The convergent operation picks up and perturbs the best-so-far solution. It decomposes the resulting solution into a set of independent partial solutions and then determines a set of subproblems which are smaller CCVRPs. Instead of directly generating solutions for the original problem, the divergent operation selects one of three operators to generate new solutions for subproblems and then assembles a solution to the original problem by using those new solutions to the subproblems. The proposed algorithm was tested on benchmark instances, some of which have more than 560 nodes. The results show that our algorithm is very effective in contrast to the existing algorithms. Most notably, the proposed algorithm can find new best solutions for 8 medium instances and 7 large instances within short time.     

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.     

The Vlasov–Poisson–Boltzmann system in the whole space: The hard potential case

This paper is concerned with the Cauchy problem on the Vlasov–Poisson–Boltzmann system for hard potentials in the whole space. When the initial data is a small perturbation of a global Maxwellian, a satisfactory global existence theory of classical solutions to this problem, together with the corresponding temporal decay estimates on the global solutions, is established. Our analysis is based on time-decay properties of solutions and a new time–velocity weight function which is designed to control the large-velocity growth in the nonlinear term for the case of non-hard-sphere interactions.     

Approximate solutions of multiobjective optimization problems

This paper provides some new results on approximate Pareto solutions of a multiobjective optimization problem involving nonsmooth functions. We establish Fritz-John type necessary conditions and sufficient conditions for approximate Pareto solutions of such a problem. As a consequence, we obtain Fritz-John type necessary conditions for (weakly) Pareto solutions of the considered problem by exploiting the corresponding results of the approximate Pareto solutions. In addition, we state a dual problem formulated in an approximate form to the reference problem and explore duality relations between them.     

一类集值映射的向量均衡问题

在拓扑向量空间内,研究了一类新的集值映射的广义向量均衡问题,利用KKM定理,证明了解的几个存在性定理,并讨论了解的性状.所得结果推广了近期一些作者的研究成果.     

Study on Sobolev type Hilfer fractional integro-differential equations with delay

In this paper, we deal with a class of nonlinear Sobolev type fractional integro-differential equations with delay using Hilfer fractional derivative, which generalized the famous Riemann–Liouville fractional derivative. The definition of mild solutions for studied problem was given based on an operator family generated by the operator pair (A, B) and probability density function. Combining with the techniques of fractional calculus, measure of noncompactness and fixed point theorem, we obtain new existence result of mild solutions with two new characteristic solution operators and the assumptions that the nonlinear term satisfies some growth condition and noncompactness measure condition. The results obtained improve and extend some related conclusions on this topic. At last, an example is given to illustrate our main results.     

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.     

Solving Ill-posed Bilevel Programs

This paper deals with ill-posed bilevel programs, i.e., problems admitting multiple lower-level solutions for some upper-level parameters. Many publications have been devoted to the standard optimistic case of this problem, where the difficulty is essentially moved from the objective function to the feasible set. This new problem is simpler but there is no guaranty to obtain local optimal solutions for the original optimistic problem by this process. Considering the intrinsic non-convexity of bilevel programs, computing local optimal solutions is the best one can hope to get in most cases. To achieve this goal, we start by establishing an equivalence between the original optimistic problem and a certain set-valued optimization problem. Next, we develop optimality conditions for the latter problem and show that they generalize all the results currently known in the literature on optimistic bilevel optimization. Our approach is then extended to multiobjective bilevel optimization, and completely new results are derived for problems with vector-valued upper- and lower-level objective functions. Numerical implementations of the results of this paper are provided on some examples, in order to demonstrate how the original optimistic problem can be solved in practice, by means of a special set-valued optimization problem.     

带p-Laplacian算子的三阶微分方程边值问题三个正解的存在性

应用Avery-Peterson不动点定理,讨论了带p-Laplacian算子的三阶三点边值问题,当非线性项f满足一定增长条件时,得到了上述边值问题至少存在三个正解的充分条件.     

Parameter-dependent systems on the half-line and free convection boundary-layers in porous media

In this paper we use a recently elaborated abstract method, for parameter-dependent ODE systems over the interval (0, ∞), to obtain existence results for the problem of self-similar solutions in boundary-layer free convection in porous media. Using a generalization of the method to exponentially decaying solutions, we are able to recover some known results, and to obtain a new branch of solutions in the case of the so-called backward boundary-layer. The arguments involve the derivation of suitable a priori estimates for the solutions of the problem.