Ground state solution for the Schrödinger equation with Hardy potential and critical Sobolev exponent
Keyword(s):
In this paper, we consider the following Schrödinger equation (0.1) − Δ u − μ u | x | 2 + V ( x ) u = K ( x ) | u | 2 ∗ − 2 u + f ( x , u ) , x ∈ R N , u ∈ H 1 ( R N ) , where N ⩾ 4, 0 ⩽ μ < μ ‾, μ ‾ = ( N − 2 ) 2 4 , V is periodic in x, K and f are asymptotically periodic in x, we take advantage of the generalized Nehari manifold approach developed by Szulkin and Weth to look for the ground state solution of (0.1).
2017 ◽
Vol 74
(6)
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pp. 1143-1157
2013 ◽
Vol 67
(1)
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pp. 227-236
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1997 ◽
Vol 12
(16)
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pp. 1127-1130
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