渐近线性椭圆方程组的非负解

本文讨论了如下一类渐近线性椭圆方程组{-Δu-μΔv=g(x,v),-Δv-λΔu=f(x,u),x∈Ω,u=v=0,x∈(e)Ω在H10(Ω)×H10(Ω)中至少存在一个非负非平凡的解对(u,v),其中Ω是RN中的一个光滑有界区域,f(x,t)和g(x,t)是Ω×R上的连续函数并且在无穷远处渐近线性.     

ON THE EXISTENCE OF NONTRIVIAL SOLUTION OF A QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEM FOR UNBOUNDED DOMAINS (2) Zero Mass Case

§0. Introduction In this paper, we continue studying the existence problem: The main difficulty we meet is generally lack of compact Sobolev embedding on unbounded domains. For the case of positive mass, we have proved in [1] the functional corresponding to (0.1) partially satisfies (P. S)_0 condition, then we may get nontrivial selution by Mountain Pass lemma. Here we shall give similar results for the case of zero mass.     

稳定平面涡旋的存在性

稳定平面涡旋由相应的Ｓｔｏｋｅｓ流函数所决定，而Ｓｔｏｋｅｓ流函数满足一个自由边值问题。本文在涡强函数是次线性增长的条件下，证明相应的自由边值问题的存在性。     

NONTRIVIAL SOLUTIONS OF HARDY-HENON TYPE ELLIPTIC SYSTEMS

In this article,the authors investigate the existence problem for Hardy Hénon type strongly indefinite elliptic systems.Existence results are obtained for such systems with superlinear suberitical nonlinearities.     

ON THE EXISTENCE OF NONTRIVIAL SOLUTION OF A QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEM FOR UNBOUNDED DOMAINS (Ⅰ) Positive Mass Case

§0. Introduction This paper as well as the subsequent one is concerned with the existence of nontrivial solution on unbounded domains for quasilinear elliptic equation: with zero-Dirichlet condition. Its energy functional is     

MULTIPLE SOLUTIONS FOR SCHR(O)DINGER EQUATIONS WITH MAGNETIC FIELD

The authors consider the semilinear SchrSdinger equation
-△Au＋Vλ（x）u= Q（x）｜u｜γ-2u in R^N,
where 1 〈 γ 〈 2＊ and γ≠ 2, Vλ= V^＋ -λV^-. Exploiting the relation between the Nehari manifold and fibrering maps, the existence of nontrivial solutions for the problem is discussed.     

EXISTENCE OF A COOPERATIVE ELLIPTIC SYSTEM INVOLVING PUCCI OPERATOR

The authors study the existence of solutions for the nonlinear elliptic system -Mλ+,Λ(D2u)=f(u,v) in Ω,-Mλ+,Λ(D2v)=g(u,v) in Ω,u≥0,v≥0 in Ω,u=v=0 on Ω,where Ω is a bounded convex domain in RN,N ≥ 2.It is shown that under some assumptions on f and g,the problem has at least one positive solution(u,v).     

EXISTENCE AND REGULARITY FOR A QUASILINEAR ELLIPTIC EQUATION INVOLVING CRITICAL EXPONENTS

In this paper, the existence of nontrivial regular solution of the Dirichlet problem for the quasilinear equation is considered.     

REGULARITY AND SYMMETRY OF SOLUTIONS OF AN INTEGRAL SYSTEM

In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u(x) = ∫R n G α(x-y)v(y) q/|y|β dy,v(x) = ∫R n G α(x-y)u(y) p/|y|β dy for x ∈ R n,where G α(x) is the kernel of Bessel potential of order α,0 ≤β < α < n,1 < p,q < n-β/β and 1/p + 1 + 1/q + 1 > n-α + β/n.We show that positive solution pairs(u,v) ∈ L p +1(R n) × L q +1(R n) are Ho¨lder continuous,radially symmetric and strictly decreasing about the origin.