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

文章研究了如下形式的 p-Laplace 方程: -Δpu+λV(x)|μ|P-2 u=f(x,μ),x∈ℝN, μ∈W1,p(ℝN), 其中参数λ>0, V∈C(RN, R+)且V -1(0)内部非空。在一些较弱的假设条件下，本文讨论了该方程非平凡解的存在性以及当λ→∞时该方程解的集中紧性，所得结果推广了相关文献的研究成果。This article concerns the p-Laplace equations: -Δpu+λV(x)|μ|P-2 u=f(x,μ),x∈ℝN, μ∈W1,p(ℝN), where λ>0 is a parameter, V∈C(RN, R+)and V -1(0) has nonempty interior. Under some mild assumptions, the existence of nontrivial solutions of the equation is obtained by using the variational method. Moreover, the concentration of solutions is also explored.