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In this paper, we study the following Kirchhoff-type equation with critical growth \begin{document}$-(a+b\int {_{\mathbb{R}^3}} |\nabla u|^2dx)\triangle u+V(x)u = λ f(x,u)+|u|^4u, \; x \; ∈\mathbb{R}^3,$ \end{document} where a>0, b>0, λ>0 and… Click to show full abstract
In this paper, we study the following Kirchhoff-type equation with critical growth \begin{document}$-(a+b\int {_{\mathbb{R}^3}} |\nabla u|^2dx)\triangle u+V(x)u = λ f(x,u)+|u|^4u, \; x \; ∈\mathbb{R}^3,$ \end{document} where a>0, b>0, λ>0 and f is a continuous superlinear but subcritical nonlinearity. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by Nehari method. Moreover, we regard b as a parameter and obtain a convergence property of the ground state solution as \begin{document}$b\searrow 0$\end{document} .
Journal Title: Communications on Pure and Applied Analysis
Year Published: 2018
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