Linear instability and nondegeneracy of ground state for combined power-type nonlinear scalar field equations with the Sobolev critical exponent and large frequency parameter
2019 ◽
Vol 150
(5)
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pp. 2417-2441
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Keyword(s):
AbstractWe consider combined power-type nonlinear scalar field equations with the Sobolev critical exponent. In [3], it was shown that if the frequency parameter is sufficiently small, then the positive ground state is nondegenerate and linearly unstable, together with an application to a study of global dynamics for nonlinear Schrödinger equations. In this paper, we prove the nondegeneracy and linear instability of the ground state frequency for sufficiently large frequency parameters. Moreover, we show that the derivative of the mass of ground state with respect to the frequency is negative.
2012 ◽
Vol 14
(05)
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pp. 1250033
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1983 ◽
Vol 82
(4)
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pp. 313-345
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Keyword(s):
2019 ◽
Vol 58
(4)
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1988 ◽
Vol 8
(4)
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pp. 431-448
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Keyword(s):
2019 ◽
Vol 45
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pp. 531-541
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2012 ◽
Vol 386
(2)
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pp. 744-762
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Keyword(s):
1983 ◽
Vol 82
(4)
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pp. 347-375
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Keyword(s):