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- W3204171965 abstract "We study the following minimization problem(0.1)eβ(b):=inf{u∈H1(R2):∫R2|u|2dx=1}Eβb(u), where Eβb(⋅) is some kind of Kirchhoff functional (the precise form is given by (1.2) below) with a periodic potential. We prove that problem (0.1) can be attained for all β≥β⁎ provided that b>0 is small enough, which is different from the case of b=0. Moreover, we are surprised to discover that the limits of minimizers of (0.1) as b→0+ for the cases of β=β⁎ and β>β⁎ are totally different. Up to rescaling, in the former case the minimizers converge to Q(x) in H1(R2), where Q(x) is the unique positive solution of −Δu+u−u3=0. However, in the latter case the minimizers converge to a minimizer of (0.1) with b=1 and potential V(x)≡0." @default.
- W3204171965 created "2021-10-11" @default.
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- W3204171965 date "2022-03-01" @default.
- W3204171965 modified "2023-10-15" @default.
- W3204171965 title "Existence and asymptotic behavior of minimizers for the Kirchhoff functional with periodic potentials" @default.
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- W3204171965 doi "https://doi.org/10.1016/j.jmaa.2021.125727" @default.
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