<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we concern with a class of quasilinear Kirchhoff-type problem. By using the Ekeland’s Variational Principle and Mountain Pass Theorem, the existence of multiple solutions is obtained. Besides, we also take this problem as an example to give the main frame of using critical point theory to find the weak solutions of nonlinear partial differential equation.</p></abstract>

In this paper, we concern with a class of quasilinear Kirchhoff-type problem. By using the Ekeland’s Variational Principle and Mountain Pass Theorem, the existence of multiple solutions is obtained. Besides, we also take this problem as an example to give the main frame of using critical point theory to find the weak solutions of nonlinear partial differential equation.

Multiple solutions of the Kirchhoff-type problem in <italic>R<sup>N</sup></italic>

Yunnan University of Finance and Economics

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Multiple solutions of the Kirchhoff-type problem in 

In this paper, we concern with a class of quasilinear Kirchhoff-type problem. By using the Ekeland’s Variational Principle and Mountain Pass Theorem, the...

Multiple solutions of the Kirchhoff-type problem in R^N

Published Online: Apr 05, 2016

Page range: 229 - 238

Received: Jan 04, 2016

Accepted: Apr 05, 2016

DOI: https://doi.org/10.21042/AMNS.2016.1.00017

Keywords
Mountain Pass Theorem, Ekeland’s Variational Principle, Kirchhoff-type problem, () sequence

© 2016 Jiahua Jin, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Multiple solutions of the Kirchhoff-type problem in RN

Published Online: Apr 05, 2016

Page range: 229 - 238

Received: Jan 04, 2016

Accepted: Apr 05, 2016

DOI: https://doi.org/10.21042/AMNS.2016.1.00017

KeywordsMountain Pass Theorem, Ekeland’s Variational Principle, Kirchhoff-type problem, () sequence

© 2016 Jiahua Jin, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Multiple solutions of the Kirchhoff-type problem in R^N

Keywords
Mountain Pass Theorem, Ekeland’s Variational Principle, Kirchhoff-type problem, () sequence