一类带权重的拟线性椭圆型方程大解的精确渐近行为

来源 :数学学报：中文版 | 被引量 : 0次 | 上传用户：tim6888

【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

【作者】

：

万海涛李希亮

【机构】

：

山东工商学院数学与信息科学学院

【出处】

：

数学学报：中文版

【发表日期】

：

2021年4期

【关键词】

：

大解精确渐近行为 Γ-变化函数

【基金项目】

：

国家自然科学基金资助项目(11971273)。

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一类带权重的拟线性椭圆型方程大解的精确渐近行为

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