# American Institute of Mathematical Sciences

March  2017, 16(2): 373-392. doi: 10.3934/cpaa.2017019

## Singular periodic solutions for the p-laplacian ina punctured domain

 1 School of Mathematics, South China University of Technology, Guangzhou 510640, China 2 Department of Mathematics, and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon, Hong Kong 3 School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

* Corresponding author: RUI HUANG.

Received  June 2015 Revised  February 2016 Published  January 2017

Abstract. In this paper we are interested in studying singular periodic solutions for the p-Laplacian in a punctured domain. We find an interesting phenomenon that there exists a critical exponent pc = N and a singular exponent qs = p-1. Precisely speaking, only if p > pc can singular periodic solutions exist; while if 1 < ppc then all of the solutions have no singularity. By the singular exponent qs = p-1, we mean that in the case when q = qs, completely different from the remaining case qqs, the problem may or may not have solutions depending on the coefficients of the equation.

Citation: Shanming Ji, Yutian Li, Rui Huang, Xuejing Yin. Singular periodic solutions for the p-laplacian ina punctured domain. Communications on Pure & Applied Analysis, 2017, 16 (2) : 373-392. doi: 10.3934/cpaa.2017019
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