一類非線性Schr?dinger方程變號解的存在性

摘要：研究了一類非線性Schr?dinger方程：－Δu+Vxu=fx，u，x∈R^N，其中f的原函數滿足的超二次條件比（AR）條件更弱.利用下降流不變集方法，證明了該方程存在變號解.

關鍵詞：Schr?dinger方程; 下降流不變集; 變號解

中圖分類號：O175 文獻標志碼：A

Existence of Sign Changing Solution fora Class of Nonlinear Schr?dinger Equations

CHEN Jin， FAN Xin-xiang

（Concord University College， Fujian Normal University， Fuzhou 350117， China）

Abstract：In this paper， we consider a class of nonlinear Schr?dinger equations －Δu+Vxu=fx，u，x∈R^N， where the super-quadratic conditions satisfied by the primitive of f are weaker than Ambrosetti-Rabinowitz type condition. By using the method of invariant sets of descending flow， we prove the existence of sign changing solution for this equation.

Key words：Schr?dinger equation; invariant set of descending flow; sign changing solution

0 引言

1 預備知識

2 主要定理的證明

2.1 算子A的定義和性質

2.2 下降流不變集

2.3 變號解的存在性

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［責任編輯：趙慧霞］