摘要
本文利用山路引理在广义Sobolev空间■^(1,F)(Ω)(其中P=(P_1,P_2,…,P_n),P_(?)≥2,i=1,2,…,n)中讨论了下面Dirichlet问题非平凡解的存在性:(?)(x,u,Du)-F_n(x,u,Du)=0,x∈Ω,证明了上述方程在(?)^(1,p)(Ω)中具有非平凡弱解,并且如果I(u)=∫_(Ω)F(x,u,Du)dx是偶泛函,则上述问题具有无穷多个非平凡弱解。
In this paper,we discuss the existence of nontrivial solutions of the following Dirichlet problem in general Sobolev space (Ω)(where P=(P_1,P_2,…,P_n),P_i≥2,i=1,2,…,n)by virtue of the Mountain Pass Lemma: We have proved that the above equation has at least one non- trivial weak solution in (Ω)。And if I(u)=_ΩF(x,u,Du)dx is an even functional then the above problem has infinity many nontrivial weak solutions.
出处
《华南理工大学学报（自然科学版）》
EI
CAS
CSCD
1990年第2期106-116,共11页
Journal of South China University of Technology(Natural Science Edition)
关键词
椭圆型方程
非平凡解
存在性
elliptic equation
weak solution
Sobolev space
quasilinear
the Mountain Pass Lemma
general Sobolev space
