数学物理学报(英文版) ›› 1987, Vol. 7 ›› Issue (1): 63-74.
陈祖墀, 沈尧天
Chen Zuchi, Shen Yaotian
摘要： Under the mild conditions by using the theory of the generalized Sobolev space and minimax theory we get the existence of solutions for a wide class of nonlinear Dirichlet problem as follows
d/dxi[Gi(x,Du)]+f(x,u)=0, x∈Q, u|∂Q=0,
where Q is a bounded domain in Rn,Gi(x,q)=∂G/∂qi, q=(q1,q2,…,qn). This equation is the Euler equation of the functional
I(u)=∫Q[G(x,Du)-F(x,u)]dx,
where
F(x,s)=∫0xf(x,t)dt.