Multi-bump solutions of -Δn = K(x)u (n+2)/(n-2) on lattices in ℝ n
2018 ◽
Vol 2018
(743)
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pp. 163-211
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Keyword(s):
Abstract We consider the following semilinear elliptic equation with critical exponent: Δ u = K(x) u^{(n+2)/(n-2)} , u > 0 in \mathbb{R}^{n} , where {n\geq 3} , {K>0} is periodic in ( x_{1} ,…, x_{k} ) with 1 \leq k < (n-2)/2. Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in {\mathbb{R}^{k}} , including infinite lattices. We also show that for k \geq (n-2)/2, no such solutions exist.
2017 ◽
Vol 262
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pp. 3107-3131
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1988 ◽
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1998 ◽
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pp. 1
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2016 ◽
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2000 ◽
Vol 163
(2)
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pp. 381-406
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