一类椭圆方程无穷多解存在性

利用H10(Ω)空间分解以及亏格和形变引理给出了半线性椭圆方程-Δu=λu+f(x,u)的D irichet问题无穷多解的存在性定理,其中λ1λ为任意给定正数.     

一类超线性椭圆方程的无穷多解

本文研究了一类超线性椭圆方程,这里的非线性项是奇的.我们不需要假设Ambrosetti-Rabinowitz条件,得到了无穷多个大能量解的存在性.我们的结论推广了邹文明最近的结果。     

R~N上临界增长的椭圆方程无穷多解的存在性

本文证明了RN上的拟线性椭圆型方程-div（|Du|p-2Du）+|u|p-2u=λ（x）·|u|α-2u+a（x）|u|s-2u+b（x）|u|p＊-2u在W1,p（RN）中无穷多解的存在性,其中N≥3,2≤p相似文献   

Infinitely Many Solutions of The Neumann Problem for Elliptic Equations Involving The p-Laplacian

In this paper, we prove the existence of an unbounded sequenceof weak solutions under an appropriate oscillating behaviourof for a Neumann problem of the type      

Infinitely Many Solutions for an Elliptic Problem with Critical Exponent in Exterior Domain

We consider the following nonlinear problem {-△u=uN＋2/N-2,u〉0 in R^N/Ω,u（x）→0 as｜x｜→＋∞,δu/δn=0 on δΩ,where Ω belong to RN,N ≥ 4 is a smooth and bounded domain and n denotes inward normal vector of δΩ. We prove that the above problem has infinitely many solutions whose energy can be made arbitrarily large when Ω is convex seen from inside （with some symmetries）.     

重调和扰动问题的无穷多解

本文考虑有界区域中具有零边值条件的重调和扰动问题,所得结论包含了[1][3][4]中的相应结果。     

一类带Sobolev-Hardy指数的椭圆型方程组无穷多球对称解的存在性

考虑了一类带Sobolev-Hardy指数的椭圆型方程组{-Δu-μu/|x|2=α/α+β|μ|α-2u|v|β/|x|s+σp/p+q|u|p-2u|v|q,x∈B,-Δu-μu/|x|2=β/α+β|μ|α|v|β-2v/|x|s+σp/p+q|u|p|v|q-2,x∈B,其中0≤μμ,-4,μ=((N-2)~2)/4,σ0,0≤s2,N6+s,α+β=2~*(s)=(2(N-s))/(N-2),p,q≥1,2≤p+q2~*(s),B■R~N为以原点为心的一个开球.利用逼近方法及喷泉定理,得到了上述方程组无穷多个球对称解的存在性.     

Infinitely Many Solutions to a Class of p-Laplace Equations

Acta Mathematicae Applicatae Sinica, English Series - In this paper, we study a class of p-Laplace equations. Using variational methods, we prove that there are two solutions and one of these...     

R~N上拟线性椭圆方程的无穷多解

运用喷泉定理研究了无界区域上拟线性椭圆方程无穷多解的存在性,推广了一些结果.     

Infinitely Many Solutions for a Mixed Doubly Eigenvalue Boundary Value Problem

In this paper, we prove the existence of infinitely many weak solutions for a mixed doubly eigenvalue boundary value problem. The approach is based on variational methods.     

含有Sobolev-Hardy临界指标的奇异椭圆方程无穷多解的存在性

该文研究如下奇异椭圆方程-Δu- μu｜x｜2 =｜u｜2 (s) -2 u｜x｜s λ｜u｜q-2 u ,u∈H10 (Ω) ,　x∈Ω ,0 ≤ μ< μ =(N- 2 ) 24 ,其中Ω是RN 中的有界区域 ,0 ∈Ω ,N≥ 3.2 (s) =2 (N -s)N- 2 ( 0 ≤s≤ 2 )是临界Sobolev Hardy指标 ,1 相似文献   

一类具有Robin条件的奇异椭圆方程无穷多解的存在性

探讨了如下的一类具有Robin条件的奇异椭圆方程:其中Ω是R~N中具有C~1边界的有界区域,0∈Ω,N≥5,2~*(s)=2(N-s)/N-2(0≤s<2)是Sobolev-Hardy临界指数,0<μ<μ~*,γ是定义在边界Ω上的单位外法向量,α(x)为非负有界函数且α(x)∈L~∞(Ω).在f的非二次条件下,利用变分方法和对偶喷泉定理,证明了:存在λ~*>0,使得对于λ∈(0,λ~*),该问题有无穷多个解{u_k}H~1(Ω)满足(1)J(u_k)<0;(2)当k→+∞时,J(u_k)→0.     

一类带扰动的非线性椭圆型方程组无穷多弱解的存在性

本文在一定条件讨论了如下一类带扰动项,且被两个Laplacian算子控制的非线性椭圆方程Dirichlet问题无穷多弱解的存在性.（-△u=∣u∣α-1∣υ∣β＋1u＋f,x∈Ω,-△υ=∣u∣α＋1∣υ∣β-1υ＋g,x∈Ω,u（x）＋ υ（x）=0,x∈（e）Ω,）其中-△u：=div（▽u）,（u,υ）∈E：=H10（Ω）× H10（Ω）,（f,g）属于E的对偶空间.     

一类不满足(AR)条件的p-Laplace方程的无穷多解

利用变分方法,得到以下p-Laplace方程-△pu+V(x)|u|p-2u = f(x,u),x ∈RN,(1)有无穷多高能量.其中1＜p＜N,势函数V(x)是RN上无界函数,非线性项f(x,u)不满足(AR)条件.     

Infinitely Many Solutions for a Class of Fractional Boundary Value Problems with Dirichlet Boundary Conditions

In this paper we prove the existence and multiplicity of weak solutions for a class of fractional boundary value problem. Our approach is based on a critical point result contained in Bonanno and Molica Bisci [Bound. Value. Probl. 2009, 1–20 (2009)].     

一类二阶常微分方程初值问题的无穷多解性

应用分离变量法,得到了一类二阶微分方程初值问题存在无穷多个非负解的充分必要条件,并给出了所有的无穷多个非负解．。     

具有奇异项的拟线性椭圆型方程组无穷多弱解的存在性

本文在一定条件下讨论了一类具有奇异项的,被两个pLaplacian算子控制的拟线性椭圆型方程组Dirichlet问题无穷多弱解的存在性.     

Infinitely Many Sign-changing Solutions for a Schroedinger Equation in R^N

We consider the existence of infinitely many sign-changing solutions for the nonlinear timeindependent schroedinger equations of the form     

Symplectic Diffeomorphisms with Infinitely Many Elliptic Periodic Points

§ 1.Introduction and Statement of Main Results　 Let M be2 n-dimensional compactmanifold with a symplectic structureω.Recall thata symplectic structureω is a non-degenerate differential2 -form on M.A diffeomorphismf that preserves symplectic formω,i.e.,f* ω=ω,is called a symplectic diffeomor-phism.Symplectic diffeomorphism arises naturally as time-one map and the Poincarémap of Hamiltonian systems.　Let Diffrω(M) denote the set of Cr diffeomorphisms on M that preserveω,with uni-f…