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- W2051799017 abstract "Let ϵ > 0 be a small parameter. In this paper, we study existence of multiple multi-bump positive solutions for the semilinear Schrödinger equation − Δ u + u = ( 1 − ϵ a ( x ) ) | u | p − 2 u , u ∈ H 1 ( R N ) , where N ⩾ 1 , 2 < p < 2 N / ( N − 2 ) if N ⩾ 3 , p > 2 if N = 1 or N = 2 , a ∈ C ( R N ) , a ( x ) > 0 for x ∈ R N , and lim | x | → ∞ a ( x ) = 0 . We also study existence of multiple multi-tower positive solutions for the prescribed scalar curvature equation − Δ u = ( 1 − ϵ K ( | x | ) ) u N + 2 N − 2 , u ∈ D 1 , 2 ( R N ) , where N ⩾ 3 , K ∈ C ( [ 0 , ∞ ) ) , K ( r ) > 0 for r > 0 , lim r → 0 K ( r ) = 0 , and lim r → ∞ K ( r ) = 0 ." @default.
- W2051799017 created "2016-06-24" @default.
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- W2051799017 date "2009-07-01" @default.
- W2051799017 modified "2023-10-16" @default.
- W2051799017 title "Multi-bump solutions and multi-tower solutions for equations on<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msup><mml:mi mathvariant=double-struck>R</mml:mi><mml:mi>N</mml:mi></mml:msup></mml:math>" @default.
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- W2051799017 doi "https://doi.org/10.1016/j.jfa.2009.02.001" @default.
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