Asymptotic Behavior and Classification of Solutions to Hartree Type Equations with Exponential Nonlinearity

被引：1

作者：

Guo, Yuxia ^{[1
]}

Peng, Shaolong ^{[2
]}

机构：

[1] Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2024年 / 34卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Hartree type equations; Exponential nonlinearity; Classification of solutions; Moving spheres; Asymptotic behavior; INVARIANT INTEGRAL-EQUATIONS; MIXED ORDER; UNIQUENESS; THEOREMS;

D O I：

10.1007/s12220-023-01470-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we are mainly concerned with the following Hartree type equations with exponential nonlinearity (-Delta)u(x) = (1/|x|(sigma) * e(pu))e(pu(x)), in R-2 where p is an element of(0, +infinity), u may change sign. We first prove the equivalence between the PDEs and the corresponding integral equations, further to get the exact asymptotic behavior of solutions to the above PDEs equation. Finally, we classify all classical solutions to the integral equations via the method of moving spheres in integral form. Consequently, we obtain the classification results of classical solutions for the PDEs.

引用

页数：21

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