Global well-posedness for nonlinear fourth-order Schrödinger equations

Boundary value problems

Xiuyan Peng¹  Jie Liu¹  Jihong Shen²  Yi Niu⁴  Mingyou Zhang⁴ 

[1] College of Automation, Harbin Engineering University, Harbin, People’College of Science, Harbin Engineering University, Harbin, People’Institutes of Biomedical Sciences, Fudan University, Shanghai, People’s Republic of China

关键词: fourth-order Schrödinger equations;    blow up;    global existence;    35Q55;    35B44;    35A01;   

DOI  :  10.1186/s13661-016-0534-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper studies a class of nonlinear fourth-order Schrödinger equations. By constructing a variational problem and the so-called invariant of some sets, we get global existence and nonexistence of the solutions.

【 授权许可】

CC BY