Abstract
In this paper, we study the existence of infinitely many solutions for a class of Kirchhoff-type problems with critical growth in $\mathbb {R}^N$. By using a change of variables, the quasilinear equations are reduced to a semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem for suitable positive parameters $\alpha , \beta $. The proofs are based on variational methods and the concentration-compactness principle.
Citation
Sihua Liang. Jihui Zhang. "Multiple solutions for Kirchhoff-type problems with critical growth in $\mathbb R^N$." Rocky Mountain J. Math. 47 (2) 527 - 551, 2017. https://doi.org/10.1216/RMJ-2017-47-2-527
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