Controlled markov processes and viscosity solutions

Controlled markov processes and viscosity solutions by W. H. Fleming and H. M. Soner. Springer-Verlag, New York (1993), 428 pp., $ 49.95. ISBN 0-387-97927-1.     

一类分数阶p（x）-拉普拉斯方程的多重解

利用临界点理论、变分方法和分数阶变指数Sobolev空间理论, 研究带有非局部系数的分数阶p(x)-拉普拉斯方程边值问题的可解性。当非线性项在零点附近次线性或在无穷远处局部超线性增长时, 得到了此类问题多重解存在的充分条件。     

Fucik Spectrum, Sign-Changing, and Multiple Solutions for Semilinear Elliptic Boundary Value Problems with Resonance at Infinity

In this paper, we use Fucik spectrum, ordinary differential equation theory of Banach spaces to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity, especially with resonance at infinity, and obtain new results on the existence of multiple solutions and sign-changing solutions with a weakening of the P.S. condition. In one case we get up to seven nontrivial solutions. The techniques have independent interest.     

Feasible descent algorithms for mixed complementarity problems

In this paper we consider a general algorithmic framework for solving nonlinear mixed complementarity problems. The main features of this framework are: (a) it is well-defined for an arbitrary mixed complementarity problem, (b) it generates only feasible iterates, (c) it has a strong global convergence theory, and (d) it is locally fast convergent under standard regularity assumptions. This framework is applied to the PATH solver in order to show viability of the approach. Numerical results for an appropriate modification of the PATH solver indicate that this framework leads to substantial computational improvements. Received April 9, 1998 / Revised version received November 23, 1998?Published online March 16, 1999     

Existence of non-trivial solution for superlinear system of integral equations and its applications

1.IntroductionTherearealotofresultsaboutHammersteinintegralequations(see[1]),butsupen-linearproblemsaredifficult;thereareonlyafewresultsaboutit.In[2,3]theauthorsstudysuperliniearintegralequations;in[4]theauthorsstudysystemofsuperlinearintegralequatio...     

一类零点为次线性的椭圆方程的可解性

该文考虑-Δu =g(x) |u|q- 2 u λ|u|p- 2 u f(x) ,x∈Ω,u| Ω =0 ,g,f∈ L∞ (Ω ) ,1 相似文献   

处理退化问题的一类SQP算法

本文对不等式优化问题提出了一个修正的序列二次规划算法(SQP).该算法适用于退化问题一积极约束梯度线性相关且严格互补条件不成立,并且算法是可行的,具有整体收敛与超线性收敛性.     

Fucik spectrum, sign-changing and multiple solutions for semilinear elliptic boundary value problems with jumping nonlinearities at zero and infinity

In this paper, Fucik spectrum, ordinary differential equation theory of Banach spaces and Morse theory are used to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity, and some new results on the existence of nontrivial solutions, multiple solutions and sign-changing solutions are obtained. In one case seven nontrivial solutions are got. The techniques have independent interest.     

1:2 Internal Resonance of Coupled Dynamic System with Quadratic and Cubic Nonlinearities

The1:2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities is studied. The normal forms of this system in1:2 internal resonance were derived by using the direct method of normal form. In the normal forms, quadratic and cubic nonlinearities were remained. Based on a new convenient transformation technique, the4-dimension bifurcation equations were reduced to3-dimension. A bifurcation equation with one-dimension was obtained. Then the bifurcation behaviors of a universal unfolding were studied by using the singularity theory. The method of this paper can be applied to analyze the bifurcation behavior in strong internal resonance on4-dimension center manifolds. Paper from Chen Yu-shu, Member of Editorial Commuttee, AMM Foundation item: the National Natural Science Foundation of China (1990510); the National Key Basic Research Special Fund (G1998020316); the Doctoral Point Fund of Education Committee of China (D09901) Biography: Chen Yu-shu (1931-)     

非线性约束最优化一族超线性收敛的可行方法

本文建立求解非线性不等式约束最优化一族含参数的可行方法．算法每次迭代仅需解一个规模较小的二次规划．在一定的假设条件下,证明了算法族的全局收敛性和超线性收敛性．