一类拟线性椭圆变分不等式解的存在性(英文)

考虑了一类p-Laplacian拟线性椭圆变分不等式问题,通过运用优化理论中的补偿法和Clark次微分性质,研究了这类椭圆变分不等式解的存在性.     

Blow-up of the Solution for a <Emphasis Type="Italic">p</Emphasis>-Laplacian Equation with Positive Initial Energy

In this paper we consider a p-Laplacian equation with the homogeneous Dirichlet boundary condition. We establish a blow-up result for certain solution with positive initial energy. This work was supported by the National Natural Science Foundation of China 10771032, and the Natural Science Foundation of Jiangsu province BK2006088.     

Asymptotic behavior of the solutions of the p -Laplacian equation

The asymptotic behavior of the solutions for p-Laplacian equations as p → ∞ is studied.     

On the Cauchy Problem of Evolution p-Laplacian Equation with Nonlinear Gradient Term

The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtained.     

Existence of positive solutions for a singular <Emphasis Type="Italic">p</Emphasis>-Laplacian differential equation

In this paper, we are concerned with the existence of positive solutions for a singular p-Laplacian differential equation
（φp（u＇））＇＋β/r φp（u＇）-γ ｜u＇｜^p/u ＋ g（r）=0,0〈r〈1,
subject to the Dirichlet boundary conditions： u（0） = u（1） =0, where φp（s） = ｜sl^P-2s,p 〉 2,β 〉0, γ〉（p-1）/p （β ＋ 1）, and g（r） ∈ C^1 [0, 1] with g（r） 〉 0 for all τ ∈ [0, 1]. We use the method of elliptic regularization, by carrying out two limit processes, to get a positive solution.     

加权流形上加权p-Laplace特征值问题的第一特征值下界估计

本文研究了加权流形上加权p-Laplacian特征值问题的第一特征值下界估计的问题.利用余面积公式、Cavalieri原理以及Federer-Fleming定理,获得了由Cheeger常数或等周常数确定的第一特征值的下界估计.     

On the Cauchy Problem of Evolution P-Laplacian Equations with Strongly Non-linear Sources When 1 < p < 2

We study the solvability of the Cauchy problem (1.1)–(1.2) for the largest possible class of initial values, for which (1.1)–(1.2) has a local solution. Moreover, we also study the critical case related to the initial value u ₀, for 1 < p < ∞. Project supported by the National Natural Science Foundation of China (19971070)     

New results of periodic solutions for a kind of Duffing type p-Laplacian equation

By using Mawhin–Manásevich continuation theorem, some new sufficient conditions for the existence and uniqueness of periodic solutions of Duffing type p-Laplacian differential equation are established, which are complement of previously known results.     

<Emphasis Type="Italic">p</Emphasis>-Laplace Operator and Diameter of Manifolds

Let be a compact Riemannian manifold without boundary. In this paper, we consider the first nonzero eigenvalue of the p-Laplacian and we prove that the limit of when is 2/d(M), where d(M) is the diameter of M. Moreover, if is an oriented compact hypersurface of the Euclidean space or , we prove an upper bound of in terms of the largest principal curvature κ over M. As applications of these results, we obtain optimal lower bounds of d(M) in terms of the curvature. In particular, we prove that if M is a hypersurface of then: . Mathematics Subject Classifications (2000): 53A07, 53C21.     

Infinitely Many Critical Points of Non-Differentiable Functions and Applications to a Neumann-Type Problem Involving the p-Laplacian

For a family of functionals in a Banach space, which are possibly non-smooth and depend also on a positive real parameter, the existence of a sequence of critical points (according to Motreanu and Panagiotopoulos (“Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities,” Nonconvex Optimization Applications, Vol. 29, Kluwer, Dordrecht, 1998, Chap. 3)) is established by mainly adapting a new technique due to Ricceri (2000, J. Comput. Appl. Math.113, 401-410). Two applications are then presented. Both of them treat the Neumann problem for an elliptic variational-hemivariational inequality with p-Laplacian.     

On the Existence of Multiple Periodic Solutions for the Vector <Emphasis Type="Italic">p</Emphasis>-Laplacian via Critical Point Theory

We study the vector p-Laplacian

Global Estimates for Non-symmetric Green Type Functions with Applications to the p-Laplace Equation

This paper presents global estimates for non-symmetric Green type functions, which are applicable to singular functions for the p-Laplace equation. This work was partially supported by Grant-in-Aid for Young Scientists (B) (No. 19740062), Japan Society for the Promotion of Science.     

Generation and Propagation of Interfaces for <Emphasis Type="Italic">p</Emphasis>-Laplacian Equations

In this paper, we consider the generation and propagation of interfaces for p-Laplacian equations with the derivative of a bi-stable potential.     

On Existence and Multiplicity of Solutions for Elliptic Equations Involving the p-Laplacian

In the present paper, the following Dirichlet problem and Neumann problem involving the p-Laplacian

含无穷拉普拉斯算子的渗流问题的李普希兹估计

本文研究含无穷拉普拉斯算子的渗流问题.运用改进的Bernstein方法和光滑逼近,分别建立了该问题严格正粘性解和非负粘性解关于空间变量的李普希兹估计.     

Existence and iteration of positive solutions for a singular two-point boundary value problem with a <Emphasis Type="Italic">p</Emphasis>-Laplacian operator

In the paper, we obtain the existence of symmetric or monotone positive solutions and establish a corresponding iterative scheme for the equation (ϕ _p (u′))′+q(t)f(u) = 0, 0 < t < 1, where ϕ _p (s):= |s| ^p−2 s, p > 1, subject to nonlinear boundary condition. The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0; 1.     

Regularity of the Extremal Solution of Some Nonlinear Elliptic Problems Involving the <Emphasis Type="Italic">p</Emphasis>-Laplacian

We consider the equation on a smooth bounded domain of with zero Dirichlet boundary conditions where p ≥ 2, λ > 0 and f satisfies typical assumptions in the subject of extremal solutions. We prove that, for such general nonlinearities f, the extremal solution u ^* belongs to L ^∞(Ω) if N < p + p/(p − 1) and if N < p(1 + p/(p − 1)). This work was partially supported by MCyT BMF 2002-04613-CO3-02.     

Positive solutions for the boundary value problems of one-dimensional p-Laplacian with delay

This paper is concerned with the existence of positive solutions for the boundary value problem of one-dimensional p-Laplacian with delay. The proof is based on the Guo–Krasnoselskii fixed-point theorem in cones.     

L r Estimates for Degenerate Elliptic Problems

We prove L ^r estimates for the Dirichlet problem –div(a(x,u,Du))=f with f in L ^q for 1q+, where the operator satisfies (|s|)|| ^p a(x,s,), with p>1. These estimates are obtained without symmetrization and are sharp in some cases.