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2017 Multiple solutions for Kirchhoff-type problems with critical growth in $\mathbb R^N$
Sihua Liang, Jihui Zhang
Rocky Mountain J. Math. 47(2): 527-551 (2017). DOI: 10.1216/RMJ-2017-47-2-527

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.

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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

Information

Published: 2017
First available in Project Euclid: 18 April 2017

zbMATH: 1373.35126
MathSciNet: MR3635373
Digital Object Identifier: 10.1216/RMJ-2017-47-2-527

Subjects:
Primary: 35J60
Secondary: 35J20, 35J25

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 2 • 2017
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