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• W3104201229 abstract "In this paper, we study the multiplicity and concentration of the positive solutions to the following critical Kirchhoff type problem: begin{equation*} -left(varepsilon^2 a+varepsilon bint_{R^3}|nabla u|^2mathrm{d} xright)Delta u + V(x) u = f(u)+u^5 {rm in } R^3, end{equation*} where $varepsilon$ is a small positive parameter, $a$, $b$ are positive constants, $V in C(mathbb{R}^3)$ is a positive potential, $f in C^1(R^+, R)$ is a subcritical nonlinear term, $u^5$ is a pure critical nonlinearity. When $varepsilon>0$ small, we establish the relationship between the number of positive solutions and the profile of the potential $V$. The exponential decay at infinity of the solution is also obtained. In particular, we show that each solution concentrates around a local strict minima of $V$ as $varepsilon rightarrow 0$." @default.
• W3104201229 created "2020-11-23" @default.
• W3104201229 creator A5045003793 @default.
• W3104201229 creator A5057209439 @default.
• W3104201229 date "2017-04-13" @default.
• W3104201229 modified "2023-10-12" @default.
• W3104201229 title "Multiplicity and concentration behavior of solutions to the critical Kirchhoff-type problem" @default.
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• W3104201229 doi "https://doi.org/10.1007/s00033-017-0803-y" @default.
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