Global existence and asymptotic behavior of the Cauchy problem for fourth-order Schrodinger equations with combined power-type nonlinearities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:392

Article

Guo, Cuihua

关键词: Fourth-order Schrodinger equation;    Combined power-type nonlinearities;    Cauchy problem;    Global existence;    Asymptotic behavior;   

DOI  :  10.1016/j.jmaa.2012.03.028

来源: Elsevier

【 摘 要 】

We study the global existence of solutions in Sobolev spaces and the asymptotic behavior for the Cauchy problem of the following fourth-order Schrodinger equation with combined power-type nonlinearities iu(t) + Delta(2)u + lambda(1)vertical bar u vertical bar(p)u + lambda(2)vertical bar u vertical bar(8/n-4) u = 0, where t epsilon R, x epsilon R-n, 8/n <= p < 8/n-4, lambda(1), lambda(2) are nonzero real numbers. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free