Biharmonic nonlinear Schrödinger equation and the profile decomposition |
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Authors: | Shihui Zhu Jian ZhangHan Yang |
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Institution: | a College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, Chinab College of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China |
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Abstract: | This paper is concerned with the Cauchy problem for the biharmonic nonlinear Schrödinger equation with L2-super-critical nonlinearity. By establishing the profile decomposition of bounded sequences in H2(RN), the best constant of a Gagliardo-Nirenberg inequality is obtained. Moreover, a sufficient condition for the global existence of the solution to the biharmonic nonlinear Schrödinger equation is given. |
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Keywords: | 35Q55 35J35 |
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