全空间上一类半线性双调和方程正解的衰减

数学物理学报 ›› 2015, Vol. 35 ›› Issue (2): 282-287.

全空间上一类半线性双调和方程正解的衰减

杨芬

武汉科技大学理学院武汉 430065

收稿日期:2013-10-27 修回日期:2014-12-11 出版日期:2015-04-25 发布日期:2015-04-25
作者简介:杨芬,E-mail:matic1232003@aliyun.com.cn
基金资助:
国家自然科学基金(11101166)和湖北省教育厅基金(D20131118)资助

Decay Rate of Solutions to An Inhomogenerous Semilinear Biharmonic Equation in Entire Space

Yang Fen

College of Science, Wuhan University of Science and Technology, Wuhan 430065

Received:2013-10-27 Revised:2014-12-11 Online:2015-04-25 Published:2015-04-25

摘要/Abstract

摘要：

研究如下非齐次双调和方程
-Δ²u +u^p +f(x)=0, x∈Rⁿ (*)
正解的存在性,其中Δ²是双调和算子, p>1, n≥5, f0. 在文献[16]的基础上, 得到: 对f给定条件, 方程(*)有一类不同于文献[16]的两种衰减的正解.

关键词: 非齐次双调和方程, 正解, 衰减

Abstract:

In this paper, we consider the existence of the positive solutions for the inhomogeneous biharmonic equation
-Δ²u +u^p +f(x)=0, x∈Rⁿ (*)
where Δ² is the biharmonic operator, p>1, n≥5, and f0 is a given nonnegative function. Based on [16], the existence of solutions with the third decay rate at infinity are established under the assumptions on f.

Key words: Inhomogeneous biharmonic equation, Positive solution, Decay rate

中图分类号:

O175.25

杨芬. 全空间上一类半线性双调和方程正解的衰减[J]. 数学物理学报, 2015, 35(2): 282-287.

Yang Fen. Decay Rate of Solutions to An Inhomogenerous Semilinear Biharmonic Equation in Entire Space[J]. Acta mathematica scientia,Series A, 2015, 35(2): 282-287.

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