摘要：In this paper, we consider the following new nonlocal Dirichlet boundary value problem: 0.1 { − ( a − b ∫ Ω | ∇ u | 2 d x ) Δ u = λ u + g ( x , u ) , x ∈ Ω , u = 0 , x ∈ ∂ Ω , $$ \textstyle\begin{cases} -(a-b\int_{\Omega} \vert \nabla u \vert ^,\,dx)\Delta u=\lambda u+g(x,u),& x\in \Omega, \\ u=0,& x\in\partial\Omega, \end{cases} $$ where a and b are positive, λ is a positive parameter, 0 ≤ λ < a λ 1 $0\leq\lambda< a\lambda_)$ , λ 1 $\lambda_)$ is the first eigenvalue of operator −Δ. Under appropriate assumptions on the function g which is of subcritical growth, we obtain a nontrivial solution.
关键词：Nonlocal problem ; Nontrivial solution ; Subcritical nonlinearity
Loading...
