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Non-Nehari manifold method for asymptotically periodic Schrdinger equations
作者姓名:TANG  XianHua
作者单位:School of Mathematics and Statistics, Central South University
基金项目:supported by National Natural Science Foundation of China(Grant No.11171351);Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120162110021)
摘    要:We consider the semilinear Schrdinger equation-△u + V(x)u = f(x, u), x ∈ RN,u ∈ H 1(RN),where f is a superlinear, subcritical nonlinearity. We mainly study the case where V(x) = V0(x) + V1(x),V0∈ C(RN), V0(x) is 1-periodic in each of x1, x2,..., x N and supσ(-△ + V0) ∩(-∞, 0)] 0 infσ(-△ +V0)∩(0, ∞)], V1∈ C(RN) and lim|x|→∞V1(x) = 0. Inspired by previous work of Li et al.(2006), Pankov(2005)and Szulkin and Weth(2009), we develop a more direct approach to generalize the main result of Szulkin and Weth(2009) by removing the "strictly increasing" condition in the Nehari type assumption on f(x, t)/|t|. Unlike the Nahari manifold method, the main idea of our approach lies on finding a minimizing Cerami sequence for the energy functional outside the Nehari-Pankov manifold N0 by using the diagonal method.

关 键 词:Schrdinger  equation  non-Nehari  manifold  method  asymptotically  periodic  ground  state  solutions  of  Nehari-Pankov  type
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