Multiple solutions of a quasilinear elliptic problem involving nonlinear boundary condition on exterior domain

In this paper, we study the multiplicity of non‐negative solutions for the quasilinear p‐Laplacian equation with the nonlinear boundary condition (1) where Δ_p denotes the p‐Laplacian operator, defined by △ _pu = div( | ? u | ^{p ? 2} ? u),1 < p < N, Ω is a smooth exterior domain in . is the outward normal derivative, . The parameters p,q,r are either or . The weight functions a(x),h(x),g(x) satisfy some suitable conditions. Using the decomposition of the Nehari manifold and the variational methods, we prove that problem (1) has at least two positive solutions provided 0 < | λ | < λ₁ for some λ₁. Copyright © 2012 John Wiley & Sons, Ltd.     

The nonlinear bilevel programming problem:formulations,regularity and optimality conditions

In this paper, we study regularity and optimality conditions for the BLPP by using a marginal function formulation, where the marginal function is defined by the optimal value function of the lower problem. We address the regularity issue by exploring the structure of the tangent cones of the feasible set of the BLPP. These regularity results indicate that the nonlinear/nonlinear BLPP is most likely degenerate and a class of nonlinear/linear BLPP is regular in the conventional sense. Existence of exact penalty function is proved for a class of nonlinear/linear BLPP. Fritz-John type optimality conditions are derived for nonlinear BLPP, while KKT type conditions are obtained for a class of nonlinear/linear BLPP in the framework of nonsmooth analysis. A typical example is examined for these conditions and some applications of these conditions are pointed out     

Regularity for nonlinear elliptic systems with dini coefficients under natural growth condition for the case: 1 < m < 2

In this article, we consider interior regularity for weak solutions to nonlinear elliptic systems of divergence type with Dini continuous coefficients under natural growth condition for the case 1 < m < 2. All estimates in the case of m ≥ 2 is no longer suitable, and we can't obtain the Caccioppoli's second inequality by using these techniques developed in the case of m ≥ 2. But the Caccioppoli's second inequality is the key to use A-harmonic approximation method. Thus, we adopt another technique introduced by Acerbi and Fcsco to overcome the difficulty and we also overcome those difficulties due to Dini condition. And then we apply the A-harmonic approximation method to prove partial regularity of weak solutions.     

Radial basis functions method for solving of a non-local boundary value problem with Neumann’s boundary conditions

In this paper, the problem of solving the two-dimensional diffusion equation subject to a non-local condition involving a double integral in a rectangular region is considered. The solution of this type of problems are complicated. Therefore, a simple meshless method using the radial basis functions is constructed for the non-local boundary value problem with Neumann’s boundary conditions. Numerical examples are included to demonstrate the reliability and efficiency of this method. Also N_e and root mean square errors are obtained to show the convergence of the method.     

小孔等离子体运动实验方法

在间接驱动惯性约束聚变的黑腔中,辐射烧蚀的高Z等离子体的流体力学运动过程对激光注入黑腔的效率、辐射场均匀性和通过诊断口的黑腔辐射温度诊断都有显著影响。为研究诊断口在黑腔辐射场中的等离子体缩口过程,用激光产生X光辐射加热低Z泡沫填充的金黑腔诊断口,以激光辐照钛平面靶产生的2～5 keV高能段窄能区X光作为背光源,用X光分幅相机获得了源靶和小孔靶两种靶型的小孔等离子体运动过程图像,研究了X光烧蚀的小孔等离子体的流体力学运动过程,探索了定量测量小孔等离子体面密度的空间分布与时间演化过程的实验诊断方法,初步给出小孔等离子体的面密度。     

CMOS电路总剂量效应最劣偏置甄别

采用电路分析和解析建模方法研究了CMOS电路中甄别总剂量效应最劣辐照与测试偏置的问题。通过引入小规模模拟电路和数字电路的例子进行具体分析,获取了不同电路的最劣偏置情况。对于数字电路,引入了敏感因子的概念用于定量计算不同辐照与测试偏置组合下电路的总剂量效应敏感程度。利用实测数据或电路仿真结果对甄别结果进行了一一验证,得到相一致的结论,证明了该研究思路的正确性。