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(shù)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(hào)解.

關(guān)鍵詞：Schr?dinger方程; 下降流不變集; 變號(hào)解

中圖分類號(hào)：O175 文獻(xiàn)標(biāo)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(yù)備知識(shí)

2 主要定理的證明

2.1 算子A的定義和性質(zhì)

2.2 下降流不變集

2.3 變號(hào)解的存在性

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［責(zé)任編輯：趙慧霞］