## Rocky Mountain Journal of Mathematics

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 18 April 2017

https://projecteuclid.org/euclid.rmjm/1492502549

Digital Object Identifier
doi:10.1216/RMJ-2017-47-2-527

Mathematical Reviews number (MathSciNet)
MR3635373

Zentralblatt MATH identifier
1373.35126

#### Citation

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. https://projecteuclid.org/euclid.rmjm/1492502549