一类带权重的拟线性椭圆型方程大解的精确渐近行为  

The Exact Asymptotic Behavior of Large Solutions to a Class of Quasilinear Elliptic Equations with Weights

作　　者：万海涛 李希亮[1] Hai Tao WAN;Xi Liang LI(School of Mathematics and Information Science,Shandong Technology and Business University,Yantai 264005,P.R.China)

机构地区：[1]山东工商学院数学与信息科学学院,烟台264005

出　　处：《数学学报（中文版）》2021年第4期551-568,共18页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11971273)。

摘　　要：本文研究了如下拟线性椭圆型方程Δpu=b(x)f(u),u(x)>0,x∈Ω大解的精确渐近行为,其中b∈C(Ω)是定义在Ω上非负非平凡的函数,f∈C[0,∞)∩C1(0,∞)是定义在[0,∞)上正的不减函数.具体而言,当Ω=RN(N≥3)时,我们通过区域截断技术和上下解方法研究了该方程整体大解在无穷远处的精确渐近行为.当Ω为带有C4-边界的有界区域时,我们研究了区域边界的平均曲率H(x)对边界行为的影响.因为(Δp)(p≠2)是非线性算子并且H(■)是定义在■Ω上的函数,因此该边界行为的计算和p=2时的情形完全不同.We study the exact asymptotic behavior of large solutions to the following equation Δpu= b(x)f(u),u(x)> 0,x ∈Ω,where b ∈ C(Ω) is non-negative and nontrivial in Ω,f ∈ C[0,∞)∩C1(0,∞) is positive and non-decreasing on(0,∞).WhenΩ=RN(N≥3),by using truncation technique and the upper and lower solution methods,we establish the exact asymptotic behavior of entire large solutions to the above equation.When is a C4-bounded domain,we revel the influence of the mean curvature H(■(x)) of■Ω to boundary behavior of large solutions.Since(Δp)(p≠2)is a non-linear operator and H(■(x)) is a variable function on■Ω,the calculation of the result is quite different from the one p=2.

关 键 词：大解 精确渐近行为 Γ-变化函数 

分 类 号：O175.25[理学—数学]