REMARKS ON THE CAUCHY PROBLEM OF KLEIN-GORDON EQUATIONS WITH WEIGHTED NONLINEAR TERMS

被引：3

作者：

Ishiwata, Michinori ^{[1
]}

Nakamura, Makoto ^{[2
]}

Wadade, Hidemitsu ^{[3
]}

机构：

[1] Osaka Univ, Grad Sch Engn Sci, Dept Syst Innovat, Toyonaka, Osaka 5608531, Japan

[2] Yamagata Univ, Fac Sci, Yamagata 9908560, Japan

[3] Kanazawa Univ, Inst Sci & Engn, Fac Mech Engn, Kanazawa, Ishikawa 9201192, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 10期

关键词：

Klein-Gordon equation; Caffarelli-Kohn-Nirenberg inequality; weighted Trudinger-Moser inequality; Brezis-Gallouet-Wainger inequality; MULTIPLE POSITIVE SOLUTIONS; DOUBLE LOGARITHMIC TERM; GLOBAL-SOLUTIONS; SCHRODINGER-EQUATIONS; ELLIPTIC-EQUATIONS; WAVE-EQUATIONS; SOBOLEV SPACE; HEAT-EQUATION; INEQUALITY;

D O I：

10.3934/dcds.2015.35.4889

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Cauchy problem of Klein-Gordon equations is considered for power and exponential type nonlinear terms with singular weights. Time local and global solutions are shown to exist in the energy class. The Caffarelli-Kohn-Nirenberg inequality and the Trudinger-Moser type inequality with singular weights are applied to the problem.

引用

页码：4889 / 4903

页数：15

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