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- W3105458274 abstract "We deal with the following fractional Schrödinger-Poisson equation with magnetic field $$varepsilon^{2s}(-{Delta})_{A/varepsilon}^{s}u+V(x)u+varepsilon^{-2t}(|x|^{2t-3}*|u|^{2})u=f(|u|^{2})u+|u|^{{2}_{s}^{*}-2}u quad text{ in } mathbb{R}^{3}, $$ where ε > 0 is a small parameter, $sin (frac {3}{4}, 1)$, t ∈ (0, 1), ${2}_{s}^{*}=frac {6}{3-2s}$ is the fractional critical exponent, $(-{Delta })^{s}_{A}$ is the fractional magnetic Laplacian, $V:mathbb {R}^{3}rightarrow mathbb {R}$ is a positive continuous potential, $A:mathbb {R}^{3}rightarrow mathbb {R}^{3}$ is a smooth magnetic potential and $f:mathbb {R}rightarrow mathbb {R}$ is a subcritical nonlinearity. Under a local condition on the potential V, we study the multiplicity and concentration of nontrivial solutions as $varepsilon rightarrow 0$. In particular, we relate the number of nontrivial solutions with the topology of the set where the potential V attains its minimum." @default.
- W3105458274 created "2020-11-23" @default.
- W3105458274 creator A5082958607 @default.
- W3105458274 date "2018-11-23" @default.
- W3105458274 modified "2023-10-16" @default.
- W3105458274 title "Multiplicity and Concentration Results for Fractional Schrödinger-Poisson Equations with Magnetic Fields and Critical Growth" @default.
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- W3105458274 doi "https://doi.org/10.1007/s11118-018-9751-1" @default.
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