ON A CLASS OF NONLINEAR SCHRODINGER-EQUATIONS

被引：1257

作者：

RABINOWITZ, PH ^{[1
]}

机构：

[1] UNIV WISCONSIN,CTR MATH SCI,MADISON,WI 53706

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 1992年 / 43卷 / 02期

关键词：

D O I：

10.1007/BF00946631

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper concerns the existence of standing wave solutions of nonlinear Schrodinger equations. Making a standing wave ansatz reduces the problem to that of studying the semilinear elliptic equation: -DELTA-u + b(x)u = f(x, u), x is-an-element-of R(n). (*) The function f is assumed to be "superlinear". A special case is the power nonlinearity f(x, z) = absolute value of z(s-1)z where 1 < s < (n + 2)(n - 2)-1. Making different assumptions on b(x), mainly at infinity, various sufficient conditions for the existence of nontrivial solutions u is-an-element-of W1,2(R(n)) are established.

引用

页码：270 / 291

页数：22

共 19 条

[1]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[2] MINIMUM-MAXIMUM PRINCIPLE FOR A CLASS OF NON-LINEAR INTEGRAL EQUATIONS [J].