一类p-Laplace方程束缚态解的存在性与集中性

Existence and Concentration of the Bound State Solutions to a Class of p-Laplace Equations

研究p-Laplace方程-Δ_(p)u+|u|p^(-2)u=Q_(n)(x)|u|q^(-2)u,x∈ℝ^(N),其中:Δ_(p)u=div(|▽u|p^(-2)▽u),1<p<N,p<q<p^(*):=Np/N-p.当n→∞时,有界函数Q_(n)(x)的自焦核supp{Q^(+)_(n)}收缩到两个不同的点.采用惩罚函数和山路引理方法证明了p-Laplace方程束缚态解的存在性和关于H^(1)范数的集中性.

In this paper,we study the following p-Laplace equation:-Δ_(p)u+|u|p^(-2)u=Q_(n)(x)|u|q^(-2)u,x∈ℝ^(N),whereΔ_(p)u=div(|▽u|p^(-2)▽u),1<p<N,p<q<p^(*):=Np/N-p.Q_(n)(x)are bounded functions with self-focusing core supp{Q^(+)_(n)}which shrinks to two different points as n→∞.Via the penalization method and the mountain pass theorem,we show the existence of the p-Laplace eauqations'bound states and the concentration of H^(1)norm bound.