期刊文献+
共找到9篇文章
< 1 >
每页显示 20 50 100
Multiplicity of Solutions for a Class of Noncooperative Elliptic Systems
1
作者 Xinxue Zhang Guanggang Liu 《Advances in Pure Mathematics》 2023年第9期610-619,共10页
In this paper, we consider the following noncooperative elliptic systems where Ω is a bounded domain in R<sup>N</sup> with smooth boundary ∂Ω, λ,δ,γ are real parameters, and . We assume that F is subq... In this paper, we consider the following noncooperative elliptic systems where Ω is a bounded domain in R<sup>N</sup> with smooth boundary ∂Ω, λ,δ,γ are real parameters, and . We assume that F is subquadratic at zero with respect to the variables u,v. By using a variant Clark’s theorem, we obtain infinitely many nontrivial solutions (u<sub>k</sub><sub></sub>,v<sub>k</sub>) with as k → ∞. Compared with the existing literature, we do not need to assume the behavior of the nonlinearity ∇F at infinity. 展开更多
关键词 Noncooperative Elliptic Systems (ps)* condition Clark’s Theorem
下载PDF
NEUMANN PROBLEMS OF A CLASS OF ELLIPTIC EQUATIONS WITH DOUBLY CRITICAL SOBOLEV EXPONENTS 被引量:3
2
作者 韩丕功 《Acta Mathematica Scientia》 SCIE CSCD 2004年第4期633-638,共6页
This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes... This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes the unit outward normal to boundary aΩ. By vaxiational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved. 展开更多
关键词 Neumann problem semilinear elliptic equation (ps)·c condition critical Sobolev exponent
下载PDF
Multiplicity of Solutions for Nonlinear Biharmonic Equation Involving Critical Parameter and Critical Exponent 被引量:2
3
作者 WANG You-jun SHEN Yao-tian 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第3期317-324,共8页
By using variational method, the multiplicity of solutions for nonlinear biharmonic equation involving critical parameter and critical exponent are established.
关键词 Hardy potential critical parameter ps condition
下载PDF
THE EXISTENCE OF SOLUTIONS OF QUASILINEAR ELLIPTIC EQUATIONS WITH CHANGE OF SIGN
4
作者 李工宝 余纯 《Acta Mathematica Scientia》 SCIE CSCD 2001年第4期469-482,共14页
This paper considers the following quasilinear elliptic problem [GRAPHICS] where Omega is a bounded regular domain in R-N (N greater than or equal to 3), N > p > 1. When g(u) satisfies suitable conditions and g(... This paper considers the following quasilinear elliptic problem [GRAPHICS] where Omega is a bounded regular domain in R-N (N greater than or equal to 3), N > p > 1. When g(u) satisfies suitable conditions and g(u)u - beta integral (u)(0) g(s)ds is unbounded, a(x) is a Holder continuous function which changes sign on Omega and integral (Omega-) \a(x)\ dx is suitably small. The authors prove the existence of a nonnegative nontrivial solution for N > p > 1. in particular, the existence of a positive solution to the problem for N > p greater than or equal to 2. Our main theorem generalizes a recent result of Samia Khanfir and Leila Lassoued (see [1]) concerning the case where p = 2. They prove also that if g(u) = \u \ (q-2)u with p < q < p* and Omega (+) = {x is an element ofQ \a(x) > 0} is a nonempty open set, then the above problem possesses infinitely many solutions. 展开更多
关键词 qasilinear elliptic equation (ps) condition mountain-pass Lemma infinite solution
下载PDF
On p-mean Curvature Operator with Critical Exponent
5
作者 FU Hong-zhuo SHEN Yao-tian YANG Jun 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第4期511-521,共11页
This paper is concerned with the existence of positive solutions of the followingDirichlet problem for p-mean curvature operator with critical exponent: -div((1 +|↓△u|^2 )p-2/2 ↓△u) = λup-1+μ u=q-1,u 〉... This paper is concerned with the existence of positive solutions of the followingDirichlet problem for p-mean curvature operator with critical exponent: -div((1 +|↓△u|^2 )p-2/2 ↓△u) = λup-1+μ u=q-1,u 〉 0,x x∈Ω,u=0,x∈ δΩ,where u ∈ W01,P is a bounded domain in R^N(N 〉 p 〉 1) with smooth boundary δΩ, 2≤p ≤q〈p,p=Np/N-p,λ,μ〉0. It reaches the conclusions that this problem has at least one positive solution in the different cases. It is discussed the existences of positivesolutions of the Dirichlet problem for the p-mean curvature operator with critical exponentby using Nehari-type duality property firstly. As p = 2, q = p, the result is correspond tothat of Laplace operator. 展开更多
关键词 mean curvature operator critical exponent ps condition dual set
下载PDF
Solutions and Multiple Solutions for p(x)-Laplacian Equations with Nonlinear Boundary Condition
6
作者 Zifei SHEN Chenyin QIAN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2009年第4期397-412,共16页
The authors study the p(x)-Laplacian equations with nonlinear boundary condi- tion. By using the variational method, under appropriate assumptions on the perturbation terms f1(x,u), f2(x,u) and h1(x), h2(x), such that... The authors study the p(x)-Laplacian equations with nonlinear boundary condi- tion. By using the variational method, under appropriate assumptions on the perturbation terms f1(x,u), f2(x,u) and h1(x), h2(x), such that the associated functional satisfies the "mountain pass lemma" and "fountain theorem" respectively, the existence and multiplicity of solutions are obtained. The discussion is based on the theory of variable exponent Lebesgue and Sobolev spaces. 展开更多
关键词 p(x)-Laplacian Nonlinear boundary condition ps condition Mountain pass lemma Fountain theorem
原文传递
EXISTENCE OF INFINITE PERIODIC SOLUTIONS TO A KIND OF p-LAPLACIAN DIFFERENTIAL EQUATION WITH DEVIATING ARGUMENTS
7
作者 Min Zhu, Xiufeng Zhang, Shiping Lu (Dept. of Math., Anhui Normal University, Wuhu 241000, Anhui) 《Annals of Differential Equations》 2010年第4期494-501,共8页
In this paper, we study a kind of p-Laplacian differential equation and obtain some new results on the existence of infinite periodic solutions.
关键词 p-Laplacian equation critical point theorem ps condition periodic solution
原文传递
Periodic Solutions for Second Order Systems at Resonance 被引量:4
8
作者 Tang Chunlei, Department of Mathematics, Southwest Normal University, Chongqing 400715, China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1998年第4期433-440,共8页
The existence and multiplicity results are obtained for periodic solutions of second order systems at resonance with unbounded nonlinearity. The proofs rely on the minimax methods and an interesting integral inequality.
关键词 PERIODIC SOLUTION RESONANCE Critical point The (ps) condition The saddle point theorem The generalized mountain pass theorem
原文传递
THE EXISTENCES OF POSITIVE SOLUTIONS FOR P-MEAN CURVATURE OPERATOR WITH SUPERCRITICAL POTENTIAL
9
作者 Fu Hongzhuo Shen Yaotian 《Journal of Partial Differential Equations》 2005年第3期193-205,共13页
This paper is concerned with the existences of positive solutions of the following Dirichlet problem for p-mean curvature operator with supercritical potential:{-div((1+| u|^2)p-2/2 u)=λu^r-1+μ(u^1q-1,|x... This paper is concerned with the existences of positive solutions of the following Dirichlet problem for p-mean curvature operator with supercritical potential:{-div((1+| u|^2)p-2/2 u)=λu^r-1+μ(u^1q-1,|x|^s),u〉0 x∈Ω,u=0 x∈ЭΩ where u∈ W0^1,P(Ω),Ω is a bounded domain in R^N(N 〉 p 〉 1) with smooth boundary ЭΩ and 0∈Ω,0 〈 q 〈p, 0≤s〈 N/p(p-q)+q, p≤r〈p*, p* = Np/N-p,μ〉0. It reaches the conclusion where this problem has two positive solutions in the different cases. It discusses the existences of positive solutions of the Dirichlet problem for the p-mean curvature operator with supercritical potential firstly. Meanwhile, it extends some results of the p-Laplace operator to that of p-mean curvature operator for p ≥2. 展开更多
关键词 Mean curvature operator Mountain Pass Principie ps condition Ekeland's variational principle.
原文传递
上一页 1 下一页 到第
使用帮助 返回顶部