摘要
设Ω是R^n中有界区域,p_i>1(i=1,2,…,n),本文探求二阶拟线性椭圆边值问题:在各向异性Sobolev空间W_(pi)~1(Ω)中有非平凡弱解的条件。应用不具“高度”的山路引理及各向异性Sobolev空间W_(pi)~1(Ω)嵌入定理,证明了上述问题相应的弱解存在定理。
Let Ω Rn be a bounded domain, p1 > 1(i = 1,2,… ,n), this paper discussed the conditions of the Dirichlet problem for the quasilinear elliptic equation
which possesses a nontrivial weak solution in . Applying the mountain pass lemma without
'height' and using the embedding theorem for the anisotropic Sobolev space ,it proved the
existence of a nontrivial weak solution for the above problem.
出处
《重庆大学学报（自然科学版）》
EI
CAS
CSCD
1992年第3期108-113,共6页
Journal of Chongqing University
基金
重庆大学青年科研基金
关键词
拟线性
椭圆型方程
非平凡解
quasilinear elliptic equation / nontrivial weak solution
anisotropic Sobolev space W( )1(Ω)
variational method
