Rocky Mountain Journal of Mathematics

Multiple solutions for Kirchhoff-type problems with critical growth in $\mathbb R^N$

Sihua Liang and Jihui Zhang

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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.

Article information

Rocky Mountain J. Math., Volume 47, Number 2 (2017), 527-551.

First available in Project Euclid: 18 April 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J20: Variational methods for second-order elliptic equations 35J25: Boundary value problems for second-order elliptic equations

Kirchhoff-type problems infinitely many solutions critical growth concentration-compactness principle variational methods


Liang, Sihua; Zhang, Jihui. Multiple solutions for Kirchhoff-type problems with critical growth in $\mathbb R^N$. Rocky Mountain J. Math. 47 (2017), no. 2, 527--551. doi:10.1216/RMJ-2017-47-2-527.

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