Journal
SCIENCE CHINA-MATHEMATICS
Volume 58, Issue 4, Pages 715-728Publisher
SCIENCE PRESS
DOI: 10.1007/s11425-014-4957-1
Keywords
Schrodinger equation; non-Nehari manifold method; asymptotically periodic; ground state solutions of Nehari-Pankov type
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Funding
- National Natural Science Foundation of China [11171351]
- Specialized Research Fund for the Doctoral Program of Higher Education of China [20120162110021]
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We consider the semilinear Schrodinger equation where f is a superlinear, subcritical nonlinearity. We mainly study the case where V(x) = V (0)(x) + V (1)(x), V (0) a C(ae (N) ), V (0)(x) is 1-periodic in each of x (1), x (2), aEuro broken vertical bar, x (N) and sup[sigma(-Delta + V (0)) a (c) (-a, 0)] < 0 < inf[sigma(-Delta + V (0)) a (c) (0, a)], V (1) a C(ae (N) ) and lim(|x|-> a) V (1)(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 N (0) by using the diagonal method.
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