Limits as p → ∞ of p-laplacian eigenvalue problems perturbed with a concave or convex term
Limits as p → ∞ of p-laplacian eigenvalue problems perturbed with a concave or convex term
复制标题
用凹项或凸项扰动的 p-拉普拉斯特征值问题的 p → ∞ 极限
DOI：
10.1007/s00526-011-0487-7
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发表时间：
2013
影响因子：
2.1
通讯作者：
E. Parini
中科院分区：
文献类型：
--
作者：
Fernando Charro;E. Parini
我们研究了方程 {−Δ pu= λp up− 1+ uq (p)− 1 in Ω, u= 0 on ∂ Ω 的正弱解序列 p→∞ 时的渐近行为，其中 λp> 0 且 1< q (p)< p 或 p< q (p)，其中 lim p→∞ q (p)/p= Q= 1。均匀极限被表征为问题 {min 的正粘度解{|∇ u (x)|− max {Λu (x), uQ (x)},−Δ∞ u (x)}= 0 (Ω)，u= 0 (∂ Ω)。对于 Λ> 0 的适当值。由于极限过程下非线性的解耦，极限问题表现出特征值问题和幂状右侧问题之间的中间行为。还获得了原始问题和极限问题的存在性和不存在性结果。
We investigate the asymptotic behaviour as p→∞ of sequences of positive weak solutions of the equation {−∆ pu= λp up− 1+ uq (p)− 1 in Ω, u= 0 on∂ Ω, where λp> 0 and either 1< q (p)< p or p< q (p), with lim p→∞ q (p)/p= Q= 1. Uniform limits are characterized as positive viscosity solutions of the problem {min {|∇ u (x)|− max {Λu (x), uQ (x)},−∆∞ u (x)}= 0 in Ω, u= 0 on∂ Ω. for appropriate values of Λ> 0. Due to the decoupling of the nonlinearity under the limit process, the limit problem exhibits an intermediate behavior between an eigenvalue problem and a problem with a power-like right-hand side. Existence and non-existence results for both the original and the limit problem are also obtained.