ENERGY METHODS FOR HARTREE TYPE EQUATIONS WITH INVERSE-SQUARE POTENTIALS

被引：11

作者：

Suzuki, Toshiyuki ^{[1
]}

机构：

[1] Tokyo Univ Sci, Dept Math, Shinjuku Ku, Tokyo 1628601, Japan

来源：

EVOLUTION EQUATIONS AND CONTROL THEORY | 2013年 / 2卷 / 03期

关键词：

SCHRODINGER-EQUATIONS; CAUCHY-PROBLEM; WAVE;

D O I：

10.3934/eect.2013.2.531

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Nonlinear Schrodinger equations with nonlocal nonlinearities described by integral operators are considered. This generalizes usual Hartree type equations (HE)(0). We construct weak solutions to (HE), a a not equal 0, even if the kernel is of non-convolution type. The advantage of our methods is the applicability to the problem with strongly singular potential a vertical bar x vertical bar(-2) as a term in the linear part and with critical nonlinearity.

引用

页码：531 / 542

页数：12

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