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• W2895954812 endingPage "2766" @default.
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• W2895954812 abstract "We investigate the existence, multiplicity and concentration of nontrivial solutions for the following fractional magnetic Kirchhoff equation with critical growth: $$begin{aligned} left( avarepsilon ^{2s}+bvarepsilon ^{4s-3} [u]_{A/varepsilon }^{2}right) (-Delta )_{A/varepsilon }^{s}u+V(x)u=f(|u|^{2})u+|u|^{2^{*}_{s}-2}u quad text{ in } mathbb {R}^{3}, end{aligned}$$ where $$varepsilon $$ is a small positive parameter, $$a, b>0$$ are fixed constants, $$sin (frac{3}{4}, 1)$$ , $$2^{*}_{s}=frac{6}{3-2s}$$ is the fractional critical exponent, $$(-Delta )^{s}_{A}$$ is the fractional magnetic Laplacian, $$A:mathbb {R}^{3}rightarrow mathbb {R}^{3}$$ is a smooth magnetic potential, $$V:mathbb {R}^{3}rightarrow mathbb {R}$$ is a positive continuous potential verifying the global condition due to Rabinowitz (Z Angew Math Phys 43:270–291, 1992), and $$f:mathbb {R}rightarrow mathbb {R}$$ is a $$C^{1}$$ subcritical nonlinearity. Due to the presence of the magnetic field and the critical growth of the nonlinearity, several difficulties arise in the study of our problem and a careful analysis will be needed. The main results presented here are established by using minimax methods, concentration compactness principle of Lions (Ann Inst H Poincaré Anal Non Linéaire 1(2):109–145, 1984), a fractional Kato’s type inequality and the Ljusternik–Schnirelmann theory of critical points." @default.
• W2895954812 created "2018-10-26" @default.
• W2895954812 creator A5082958607 @default.
• W2895954812 date "2019-04-30" @default.
• W2895954812 modified "2023-10-14" @default.
• W2895954812 title "Multiplicity and Concentration of Solutions for a Fractional Kirchhoff Equation with Magnetic Field and Critical Growth" @default.
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• W2895954812 doi "https://doi.org/10.1007/s00023-019-00803-5" @default.
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