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- W2608293962 abstract "In this paper, we show the existence of solutions for the coupled Dirac system$left{ begin{aligned}Du=frac{partial H}{partial v}(x,u,v)hspace{4mm} {rm on}hspace{2mm}M,Dv=frac{partial H}{partial u}(x,u,v)hspace{4mm} {rm on}hspace{2mm}M,end{aligned} right.$where $M$ is an $n$-dimensional compact Riemannian spin manifold, $D$ is the Dirac operator on $M$, and $H:Sigma Moplus Sigma Mto mathbb{R}$ is a real valued superquadratic function of class $C^1$ in the fiber direction with subcritical growth rates. Our proof relies on a generalized linking theorem applied to a strongly indefinite functional on a product space of suitable fractional Sobolev spaces. Furthermore, we consider the $mathbb{Z}_2$-invariant $H$ that includes a nonlinearity of the form$H(x,u,v)=f(x)frac{|u|^{p+1}}{p+1}+g(x)frac{|v|^{q+1}}{q+1},$where $f(x)$ and $g(x)$ are strictly positive continuous functions on $M$ and $p, q>1$ satisfy$frac{1}{p+1}+frac{1}{q+1}>frac{n-1}{n}.$In this case we obtain infinitely many solutions of the coupled Dirac system by using a generalized fountain theorem." @default.
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- W2608293962 date "2017-01-01" @default.
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- W2608293962 title "On coupled Dirac systems" @default.
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- W2608293962 doi "https://doi.org/10.3934/dcds.2017185" @default.
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