Multiplicity and symmetry results for a nonlinear Schrödinger equation with non‐local regional diffusion |
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Authors: | César E Torres Ledesma |
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Institution: | Departamento de Matemáticas, Universidad Nacional de Trujillo, Trujillo, Peru |
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Abstract: | In this paper, we are interested in the nonlinear Schrödinger equation with non‐local regional diffusion (1) where 0 < α < 1 and is a variational version of the regional Laplacian, whose range of scope is a ball with radius ρ(x) > 0. The novelty of this paper is that, assuming f is of subquadratic growth as |u|→+∞, we show that 1 possesses infinitely many solutions via the genus properties in critical point theory. Furthermore, if f(x,u) = γa(x)|u|γ ? 1, where is a nonincreasing radially symmetric function, then the solution of 1 is radially symmetric. Copyright © 2015 John Wiley & Sons, Ltd. |
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Keywords: | Liouville– Weyl fractional derivative fractional Sobolev space critical point theory comparison argument ground state |
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