Fractional elliptic equations with critical exponential nonlinearity
2016 ◽
Vol 5
(1)
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pp. 57-74
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Keyword(s):
AbstractWe study the existence of positive solutions for fractional elliptic equations of the type (-Δ)1/2u = h(u), u > 0 in (-1,1), u = 0 in ℝ∖(-1,1) where h is a real valued function that behaves like eu2 as u → ∞ . Here (-Δ)1/2 is the fractional Laplacian operator. We show the existence of mountain-pass solution when the nonlinearity is superlinear near t = 0. In case h is concave near t = 0, we show the existence of multiple solutions for suitable range of λ by analyzing the fibering maps and the corresponding Nehari manifold.
2017 ◽
Vol 19
(06)
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pp. 1750018
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2018 ◽
Vol 22
(01)
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pp. 1850078
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1994 ◽
Vol 124
(6)
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pp. 1177-1191
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2006 ◽
Vol 11
(4)
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pp. 323-329
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2013 ◽
Vol 66
(7)
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pp. 1245-1260
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1982 ◽
pp. 133-155
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