下线性与混合线性情况下的无限域上非线性p-Laplacian问题

Sublinear and Mixed Linear p-Laplacian Problems on Unbounded Domain

研究了无限域上的非线性 p Laplacian问题 .利用变分极值理论证明了如果下线性以及混合线性情况满足一定条件则非线性 p Laplacian问题有正解 .

The authors consider the p-Laplacian problem: f(x,u)=-div(a(x)u p-2u)+b(x)u p-2u,x∈Ω,u_ Ω=0, lim|x|→∞u=0, where 1<p<n,Ω(R n) is an exterior domain. Under certain conditions,the authors show the existence of solutions for the sublinear and mixed sub-superlinear problems via critical point theory.