Abstract
We are concerned with the semi-linear Schrodinger equation: - Δ u + V ( x ) u = K ( x ) | u | 2 * - 2 u + g ( x , u ) u ∈ H 1 ( R N ) where N ⩾ 3 , V ( x ) is a continuous function such that the spectrum σ ( - Δ + V ( x ) ) of - Δ + V ( x ) in L 2 ( R N ) has a negative part, 2 * = 2 N / ( N - 2 ) is the critical Sobolev exponent, K ( x ) is a bounded positive function, g is of subcritical growth. We prove that under suitable hypotheses the equation has a nontrivial solution.
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