p-Laplacian

摘要： We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).

摘要： 运用 Krasnoselskii 不动点定理, 本文考虑 p-Laplacian 混合边值问题 负的径向凸解的存在性, 其中B1 = {x ∈ ℝN: x p(s) = sp−2s, p 1,f : [0,1] ×[0,∞) → [0,∞) 连续.

摘要： In this paper,we deal with a singular quasilinear critical elliptic equation of Lichnerowicz type involving the p-Laplacian operator.With the help of the subcritical approach from the variational method,we obtain the non-existence,existence,and multiplicity results under some given assumptions.

摘要： 该文研究了一类带有p-Laplacian和Neumann边值条件的次线性双调和问题.利用变分方法得到了该问题变号解的存在性与多重性.

摘要： 该文考虑了一类具有偏差变元的奇性p-Laplacian Lienard型方程 (ψp(xt(t)))t + f(x(t))xt(t) + g(t, x(t ― σ(t))) = e(t),其中g(x)在原点处具有吸引奇性.通过应用Manasevich-Mawhin连续定理和一些分析方法, 证明了这个方程周期解的存在性.%In this paper, we consider a kind of p-Laplacian singular Lienard equation with time-dependent deviating argument (ψp(xt(t)))t + f(x(t))xt(t) + g(t, x(t ― σ(t))) = e(t), where g has a attractive singularity at x = 0. By applications of Manasevich-Mawhin continuation theorem and some analysis skills, sufficient conditions for the existence of periodic solution is established.

摘要： A modified wavelet quadrature method was developed through Coiflet approximation of functions in a bounded interval.A boundary extension technique was adopted to prevent the so-called boundary jumping phenomena,which arose from direct approximation of the interval bounded functions using wavelet bases;and relations among different-order derivatives were established,so that the original differential equation could be expressed by the highest-order derivatives as an unknown function.Several typical numerical examples were presented to demonstrate the accuracy and efficiency of the proposed method.%通过有限区间上的Coiflet函数逼近,给出了一种改进的小波求积方法.采用边界延拓技术以抑制出现在直接使用小波基近似的区间有界函数的边界跳跃现象,建立了不同阶导数的关系.最高阶导数可作为未知函数表达原微分方程.给出了多个典型的数值算例证明了该方法的计算精度与效率.

摘要： 研究一类带有p-Laplacian算子的分数阶微分方程的边值问题.首先给出了边值问题解的表达式,并分析了表达式中的格林函数的性质;然后利用锥上的Guo-Krasnosel'skii不动点定理证明了该边值问题正解的存在性.

摘要： 以特征值估计的Li-猜想与Yang-猜想的提出与发展为基础,分类研究总结典型的黎曼流形上Laplace算子主特征值估计条件改变时估计值上下界的变化,得到最新的更加精确的估计结果。主要研究一般黎曼流形上的p-Laplacian的主特征值估计;将黎曼度量推广到Finsler流形上的主特征值估计;以及引入势函数后特征函数改变而得到新的Laplace型算子——Schrödinger算子的主特征值的估计。特征值估计的研究体现出微分流形与广义相对论的紧密联系,能够促进量子力学中能谱等问题的解决,为量子力学、量子光学和固体物理提供新方法。

摘要： 研究了一维p-Laplacian动力方程{(Φ_p(u′(t))′+h(t)f(t,u(t),u′(t))=0,u(0)=u(1)=ω,u′(0)=-u′(1),t∈[0,1]两点边值问题对称正解的存在性.利用锥压缩和锥拉伸不动点定理,得到了该边值问题一个对称正解的存在性定理.