Three solutions to inequalities of Dirichlet problem driven by p（x）-Laplacian

A class of nonlinear elliptic problems driven by p（x）-Laplacian with a nonsmooth locally Lipschitz potential is considered.By applying the version of the nonsmooth three-critical-point theorem,the existence of three solutions to the problems is proved.     

SET-VALUED EXTENSION OF OPERATORS VIA STEINER SELECTIONS (Ⅰ)-THEORETICAL RESULTS

A way to extend operators in spaces of continuous functions to spaces of continuous set-valued functions is proposed. This extension is developed through the Steiner selections of the set-valued functions. Their properties and characteristics of the convergence of sequences of operators of this class are studied. In Part Ⅱ of this series some applications to approximation theory will be shown.     

Asymptotic Behavior of Quasi-Autonomous Expansive Type Evolution Systems in a Hilbert Space

We introduce the notion of almost expansive sequences and curves and study their ergodic and asymptotic properties in a Hilbert space H. We apply our results to study the asymptotic behavior of solutions to the quasi-autonomous expansive type evolution system (du/dt)(t) + f(t) ∈ Au(t) on [0, ∞).     

g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions

A new class of g-η-monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-monotone mappings are introduced. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented.An iterative algorithm for approximating the solutions of generalized implicit variationallike inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved.     

System of set-valued mixed quasi-variational-like inclusions involving H-η-monotone operators in Banach spaces

A new system of the set-valued mixed quasi-variational-like inclusions (SS-MQVLI) involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone opera-tors, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new re-sults have extended and improved previous results.     

HIGH-ORDER BEM FORMULATIONS FOR STRONGLY NON-LINEAR PROBLEMS GOVERNED BY QUITE GENERAL NON-LINEAR DIFFERENTIAL OPERATORS. PART 2: SOME 2D EXAMPLES

In this paper the general BEM proposed previously by Liao is applied to solve some 2D strongly non-linear differential equations, even including those whose governing equations and boundary conditions do not contain any linear terms. It is shown that the proposed general BEM is really valid for general non-linear problems, so that it can be applied to solve high-dimensional, strongly non-linear problems in engineering. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 863–873, 1997.     

广义特征值问题的Collatz包含定理

工程中已发展了许多矩阵特征值问题的近似求解方法,由Duncley法给出固有频率基频的下界,Rayleigh-Ritz近似法建立的方程,给出基频的上界,以及通常的矩阵迭代法给出的矩阵的固有频率程序中是以某一元素迭代前后比值确定的,这样实际上很难说是上界或下界。Collatz包含定理仅适用于对称标准特征值问题,可以给出特征值上、下界。采用矩阵Cholesky三角分解的原理,把Collatz包含定理推广到适用于具有对称矩阵的一般结构系统的广义征值问题,对于分解刚度矩阵或质量矩阵可给出基频,或最高因有频率。为了验证理论的正确性,给出了算例。     

HIGH-ORDER BEM FORMULATIONS FOR STRONGLY NON-LINEAR PROBLEMS GOVERNED BY QUITE GENERAL NON-LINEAR DIFFERENTIAL OPERATORS

In this paper the basic idea of homotopy in topology is applied to give a kind of high-order BEM formulation for general non-linear problems governed by non-linear differential operators which need not contain any linear operators at all. As a result, the traditional BEM for non- linear problems is just a special case of the proposed method. Three simple examples are used to show the effectiveness of the proposed quite general BEM for non-linear problems.     

Stability properties of equilibrium sets of non-linear mechanical systems with dry friction and impact

In this paper, we will give conditions under which the equilibrium set of multi-degree-of-freedom non-linear mechanical systems with an arbitrary number of frictional unilateral constraints is attractive. The theorems for attractivity are proved by using the framework of measure differential inclusions together with a Lyapunov-type stability analysis and a generalisation of LaSalle’s invariance principle for non-smooth systems. The special structure of mechanical multi-body systems allows for a natural Lyapunov function and an elegant derivation of the proof. Moreover, an instability theorem for assessing the instability of equilibrium sets of non-linear mechanical systems with frictional bilateral constraints is formulated. These results are illustrated by means of examples with both unilateral and bilateral frictional constraints.