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- W4287762355 abstract "We look for multiple solutions $mathbf{U}colonmathbb{R}^3tomathbb{R}^3$ to the curl-curl problem [ nablatimesnablatimesmathbf{U}=h(x,mathbf{U}),qquad xinmathbb{R}^3, ] with a nonlinear function $hcolonmathbb{R}^3timesmathbb{R}^3tomathbb{R}^3$ which has subcritical growth at infinity or is critical in $mathbb{R}^3$, i.e. $h(x,mathbf{U})=|mathbf{U}|^4mathbf{U}$. If $h$ is radial in $mathbf{U}$ and $a=1$ below, then we show that the solutions to the problem above are in one to one correspondence with the solutions to the following Schrodinger equation [ -Delta u+frac{a}{r^2}u=f(x,u),qquad ucolonmathbb{R}^3to mathbb{R}, ] where $x=(y,z)in mathbb{R}^2times mathbb{R}$, $r=|y|$ and $a ge 0$. In the critical case, the multiplicity problem for the latter equation has been studied only in the autonomous case $a=0$ and the available methods seem to be insufficient for the problem involving the singular potential, i.e., $aneq 0$, due to the lack of conformal invariance. Therefore we develop methods for the critical curl-curl problem and show the multiplicity of bound states for both equations. In the subcritical case, instead, studying the Schrodinger equation in higher dimensions, we find infinitely many bound states for both problems." @default.
- W4287762355 created "2022-07-26" @default.
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- W4287762355 date "2020-06-05" @default.
- W4287762355 modified "2023-10-12" @default.
- W4287762355 title "Multiple solutions to cylindrically symmetric curl-curl problems and related Schrodinger equations with singular potentials" @default.
- W4287762355 doi "https://doi.org/10.1137/22m1494786" @default.
- W4287762355 hasPublicationYear "2020" @default.
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