一类超线性椭圆方程的非平凡解Nontrivial Solution for a Semilinear Elliptic Equation
林美琳;陈建清;
摘要(Abstract):
应用环绕定理以及精确估计来讨论一类在零点有奇性的超线性椭圆方程:-Δu+k(x)x 2u=u 2*-2u,u∈D1,0 2(Ω),其中k(x)满足一定的条件,2*=2N/(N-2)(N≥3),可以得到一个非平凡解的存在性.
关键词(KeyWords): 非平凡解;超线性椭圆方程;环绕定理
基金项目(Foundation): 国家自然科学基金资助项目(10501006)
作者(Authors): 林美琳;陈建清;
参考文献(References):
- [1]Brézis H,Nirenberg L.Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents[J].Comm Pure Appl Math,1983,36:437-477.
- [2]Capozzi A,Fortunato D,Palmieri G.An existence result fornonlinear elliptic problems involving critical Sobolevexponent[J].Ann Inst H PoincaréAnal Nor Linéaire,1985,2:463-470.
- [3]Chen Shaowei,Li Yongqing.Nontrivial solution for a semilinear elliptic equation in unbounded domain with criticalSobolev exponent[J].J Math Anal Appl,2002,272:393-406.
- [4]Chen Jianqing.Multiple positive solutions for a class of nonlinear elliptic equations[J].J Math Anal Appl,2004,295:341-354.
- [5]Willem M.Minimax theorems[M].Bostons:Birkha。user,1996.