Sobolev-Hardy不等式与临界双重调和问题

该文讨论一类带有奇异系数的双重调和方程{△^2u-μu/|x|^s=f(x,u),x∈Ω,u=δu/δv=0,x∈δΩ，这里Ω包含R^N是包含0的有界光滑区域，u∈H0^2(Ω），μ∈R是参数，0≤s≤2,△^2=△△表示双重拉普拉斯算子，当f(x,u)=u^p,p=2N/N-4时，上述问题就是一个临界双重调和问题，该文运用Sobolev-Hardy不等式和变分方法，得到它的解的存在性的一些结果。     

一类Fisher方程的行波解

本文讨论了一类广义Fisher方程,得到了它的多个显式行波解.     

一种奇异临界椭圆方程的非平凡解

该文研究了一类带有Sobolev-Hardy临界指数的半线性椭圆方程,运用变分理论中的环绕定理证明了方程非平凡解的存在性     

SOLUTIONS FOR THE QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY-SOBOLEV EXPONENTS

In this article, we study the quasilinear elliptic problem involving critical Hardy Sobolev exponents and Hardy terms. By variational methods and analytic techniques, we obtain the existence of sign-changing solutions to the problem.     

关于一个反应扩散方程的两个结果

本文讨论了一个反应扩散方程的行波解以及一个平面三次系统的全局相图．     

SOLUTIONS TO ELLIPTIC SYSTEMS INVOLVING DOUBLY CRITICAL NONLINEARITIES AND HARDY-TYPE POTENTIALS

In this article,an elliptic system is investigated,which involves Hardy-type potentials,critical Sobolev-type nonlinearities,and critical Hardy-Sobolev-type nonlinearities.By a variational global-compactness argument,the Palais-Smale sequences of related approximation problems is analyzed and the existence of infinitely many solutions to the system is established.     

一个反应扩散方程的显式波前解与一个平面三次微分系统的全局分析

该文讨论了反应扩散方程 u_t=u_(xx) u(1-u)(u-a)(1)的行波解U(z)=U(x ct),这里0相似文献   

EXISTENCE OF POSITIVE SOLUTIONS TO QUASI-LINEAR EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT

This paper is concerned with the quasi-linear equation with critical SobolevHardy exponent where Ω RN(N ≥ 3) is a smooth bounded domain, 0 ∈Ω, 0 ≤ s ＜ p, 1 ＜ p ＜ N,p* (s) :=p(N- s)/N-p is the critical Sobolev-Hardy exponent, λ＞ 0,p ≤ r ＜ p* ,p* := Np/N-p is the critical Sobolev exponent, μ＞ 0, 0 ≤ t ＜ p, p ≤ q ＜ p* (t) = P(N-t)/N-p.The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.     

一类带奇异系数椭圆方程解的存在性

本文运用变分方法及Hardy不等式讨论了一类带奇异系数的临界椭圆方程，证明了在一定条件下方程解的存在性。