Positive ground state solutions for fractional Kirchhoff type equations with critical growth

2018 ◽  
Vol 42 (3) ◽  
pp. 1018-1038
Author(s):  
Wentao Huang ◽  
Xiao Luo
Keyword(s):  
Ground State ◽  
Critical Growth ◽  
Ground State Solutions ◽  
Kirchhoff Type

scholarly journals Ground state solutions for Kirchhoff-type equations with a general nonlinearity in the critical growth

2018 ◽  
Vol 7 (4) ◽  
pp. 535-546 ◽  
Author(s):  
Li-Ping Xu ◽  
Haibo Chen
Keyword(s):  
Variational Methods ◽  
Ground State ◽  
Critical Growth ◽  
Ground State Solutions ◽  
Kirchhoff Type ◽  
General Nonlinearity

AbstractIn this paper, we concern ourselves with the following Kirchhoff-type equations:\left\{\begin{aligned} \displaystyle-\biggl{(}a+b\int_{\mathbb{R}^{3}}\lvert% \nabla u\rvert^{2}\,dx\biggr{)}\triangle u+Vu&\displaystyle=f(u)\quad\text{in % }\mathbb{R}^{3},\\ \displaystyle u&\displaystyle\in H^{1}(\mathbb{R}^{3}),\end{aligned}\right.where a, b and V are positive constants and f has critical growth. We use variational methods to prove the existence of ground state solutions. In particular, we do not use the classical Ambrosetti–Rabinowitz condition. Some recent results are extended.

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