Electron. J. Differential Equations, Vol. 2017 (2017), No. 84, pp. 1-14.

Multiple solutions of a p-Kirchhoff equation with singular and critical nonlinearities

Qin Li, Zuodong Yang, Zhaosheng Feng

In this article, we explore the existence of multiple solutions for a p-Kirchhoff equation with the nonlinearity containing both singular and critical terms. By means of the concentration compactness principle and Ekeland's variational principle, we obtain two positive weak solutions.

Submitted January 6, 2016. Published March 27, 2017.
Math Subject Classifications: 35J60, 35B09, 35J91.
Key Words: Weak solution; p-Kirchhoff equation; p-Laplacian; quasilinear elliptic equation; variational principle; concentration compactness principle.

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Qin Li
School of Statistics and Applied Mathematics
Anhui University of Finance and Economics
Bengbu, Anhui 233030, China
email: 294973245@qq.com
Zuodong Yang
School of Teacher Education
Nanjing Normal University
Nanjing, Jiangsu 210097, China
email: yangzuodong@njnu.edu.cn
Zhaosheng Feng
Department of Mathematics
University of Texas-Rio Grande Valley
Edinburg, TX 78539, USA
email: zhaosheng.feng@utrgv.edu

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