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Register a new userCylindrically Symmetric Ground State Solutions for Curl-Curl Equations with Critical Exponent
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Xiaoyu Zeng
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We study the following nonlinear critical curl-curl equation begin{equation}label{eq0.1} ablatimes ablatimes U +V(x)U=|U|^{p-2}U+ |U|^4U,quad xin mathbb{R}^3,end{equation} where $V(x)=V(r, x_3)$ with $r=sqrt{x_1^2+x_2^2}$ is 1-periodic in $x_3$ direction and belongs to $L^infty(R^3)$. When $0 otin sigma(-Delta+frac{1}{r^2}+V)$ and $pin(4,6)$, we prove the existence of nontrivial solution for (ref{eq0.1}), which is indeed a ground state solution in a suitable cylindrically symmetric space. Especially, if $ sigma(-Delta+frac{1}{r^2}+V)>0$, a ground state solution is obtained for any $pin(2,6)$.
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