Nontrivial solutions for p-Laplacian systems

摘要

The paper deals with the existence and nonexistence of nontrivial nonnegative solutions for the sublinear quasilinear system div(|▽ui|p-2▽ui)+λfi(u1,...,Un)=0 in Ω, ui+0, on eΩ,i=1,...,n, where p>1, Ω is a bounded domain in (N2) with smooth boundary, and fi, i=1,…,n, are continuous, nonnegative functions. Let u=(u1,…,un), we prove that the problem has a nontrivial nonnegative solution for small λ>0 if one of is infinity. If, in addition, all is zero, we show that the problem has a nontrivial nonnegative solution for all λ>0. A nonexistence result is also obtained.