Positive solutions for a quasilinear Schrödinger equation involving Hardy potential and critical exponent
2014 ◽
Vol 16
(06)
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pp. 1450034
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Keyword(s):
We are concerned with positive solutions of a quasilinear Schrödinger equation with Hardy potential and critical exponent. Different from the semilinear equation, the Hardy term in our equation is not only singular, but also nonlinear. It seems unlikely to get solutions for our equation in H1(ℝN) ∩ L∞(ℝN) by using Nehari method as Liu–Liu–Wang [Ground states for quasilinear Schrödinger equations with critical growth, Calc. Var. Partial Differential Equations 46 (2013) 641–669]. In this paper, by transforming the quasilinear equation to a semilinear equation, we established the existence of positive solutions for the quasilinear Schrödinger equation in H1(ℝN) under suitable conditions.
2018 ◽
Vol 44
◽
pp. 118-127
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2016 ◽
Vol 15
(4)
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pp. 1309-1333
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