[1] Zhang Hui, Zhang Fubao,. Ground states for asymptotically periodic quasilinearSchrödinger equations with critical growth [J]. Journal of Southeast University (English Edition), 2013, 29 (3): 352-354. [doi:10.3969/j.issn.1003-7985.2013.03.022]

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Ground states for asymptotically periodic quasilinearSchrödinger equations with critical growth()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

29

Issue:

2013 3

Page:

352-354

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2013-09-20

Info

Title:

Ground states for asymptotically periodic quasilinearSchrödinger equations with critical growth

Author(s):

Zhang Hui;  Zhang Fubao

Department of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

quasilinear Schrö;  dinger equation;  variational method;  ground state;  critical growth

PACS:

O175.2

DOI:

10.3969/j.issn.1003-7985.2013.03.022

Abstract:

For a class of asymptotically periodic quasilinear Schrödinger equations with critical growth, the existence of ground states is proved. First, applying a change of variables, the quasilinear Schrödinger equations are reduced to semilinear Schrödinger equations, in which the corresponding functional is well defined in H¹(R^NN). Moreover, there is a one-to-one correspondence between ground states of the semilinear Schrödinger equations and the quasilinear Schrödinger equations. Then the mountain-pass theorem is used to find nontrivial solutions for the semilinear Schrödinger equations. Finally, under certain monotonicity conditions, using the Nehari manifold method and the concentration compactness principle, the nontrivial solutions are found to be exactly the same as the ground states of the semilinear Schrödinger equations.

References:

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[3] Liu J, Wang Y, Wang Z. Solutions for quasilinear Schrödinger equations via the Nehari method [J]. Communications in Partial Differential Equations, 2004, 29(5/6): 879-901.
[4] Liu X, Liu J, Wang Z. Ground states for quasilinear Schrödinger equation with critical growth [J]. Calculus of Variations and Partial Differential Equations, 2013, 46(3/4): 641-669.
[5] Silva E A B, Vieira G F. Quasilinear asymptotically periodic elliptic equations with critical growth [J]. Calculus of Variations and Partial Differential Equations, 2012, 39(1/2): 1-33.
[6] Szulkin A, Weth T. The method of Nehari manifold [C]//Handbook of Nonconvex Analysis and Applications. Boston, USA: International Press, 2010: 597-632.
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[8] Silva E A B, Vieira G F. Quasilinear asymptotically periodic Schrödinger equations with subcritical growth [J]. Nonlinear Analysis: Theory, Methods and Applications, 2010, 72(6): 2935-2949.

Memo

Memo:

Biographies: Zhang Hui(1987—), female, graduate; Zhang Fubao(corresponding author), male, doctor, professor, zhangfubao@seu.edu.cn.
Foundation item: The Scientific Innovation Research of College Graduates in Jiangsu Province(No.CXLX_0069).
Citation: Zhang Hui, Zhang Fubao. Ground states for asymptotically periodic quasilinear Schrödinger equations with critical growth[J].Journal of Southeast University(English Edition), 2013, 29(3):352-354.[doi:10.3969/j.issn.1003-7985.2013.03.022]

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