Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity
2016 ◽
Vol 15
(05)
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pp. 699-729
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Keyword(s):
This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method.
2012 ◽
Vol 53
(8)
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pp. 083702
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2014 ◽
Vol 411
(2)
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pp. 530-542
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2013 ◽
Vol 54
(3)
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pp. 031501
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2015 ◽
Vol 95
(8)
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pp. 1616-1634
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2015 ◽
Vol 293
◽
pp. 238-251
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2016 ◽
Vol 97
(2)
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pp. 255-273
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