On the fractional Schrödinger problem with non‐symmetric potential |
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| Authors: | Jing Yang |
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| Institution: | School of Mathematics and Statistics, Central China Normal University, Wuhan, China |
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| Abstract: | We study the semilinear equation ![urn:x-wiley:mma:media:mma3309:mma3309-math-0001]( "urn:x-wiley:mma:media:mma3309:mma3309-math-0001") where 0 < s < 1,  , V(x) is a sufficiently smooth non‐symmetric potential with  , and ? > 0 is a small number. Letting U be the radial ground state of (?Δ)sU + U ? Up=0 in  , we build solutions of the form ![urn:x-wiley:mma:media:mma3309:mma3309-math-0005]( "urn:x-wiley:mma:media:mma3309:mma3309-math-0005") for points ?j,j = 1,?,m, using a Lyapunov–Schmidt variational reduction. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | fractional Laplacian non‐symmetric potential Schrö dinger equation reduction |
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