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arxiv: 1402.1902 · v1 · pith:7MMADJ4Unew · submitted 2014-02-09 · 🧮 math.AP

Infinitely many positive solutions for nonlinear fractional Schr\"{o}dinger equations

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keywords positivedingerfractionalinfinitelymanynonlinearschrsolutions
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We consider the following nonlinear fractional Schr\"{o}dinger equation $$ (-\Delta)^su+u=K(|x|)u^p,\ \ u>0 \ \ \hbox{in}\ \ R^N, $$ where $K(|x|)$ is a positive radial function, $N\ge 2$, $0<s<1$, $1<p<\frac{N+2s}{N-2s}$. Under some asymptotic assumptions on $K(x)$ at infinity, we show that this problem has infinitely many non-radial positive solutions, whose energy can be made arbitrarily large.

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