Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-23T22:07:43.021Z Has data issue: false hasContentIssue false

A NOTE ON RADIAL SYMMETRY FOR AN INTEGRAL EQUATION OF WOLFF TYPE

Published online by Cambridge University Press:  20 February 2019

YUN WANG*
Affiliation:
Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China email wangjiaqidouqi@foxmail.com
LIXIN TIAN
Affiliation:
Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China email tianlixin@njnu.edu.cn

Abstract

We prove that positive solutions of an integral equation of Wolff type are radially symmetric and decreasing about some point in $R^{n}$. The hypotheses allow a wider range of exponents and are easier to apply than those in previous work.

Type
Research Article
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This research was supported by Innovation Project for Graduate Student Research of Jiangsu Province (Grant No. KYCX17 1053).

References

Chen, W. and Li, C., ‘Radial symmetry of solutions for some integral systems of Wolff type’, Discrete Contin. Dyn. Syst. 30 (2011), 10831093.Google Scholar
Chen, W., Li, C. and Ou, B., ‘Qualitative properties of solutions for an integral equation’, Discrete Contin. Dyn. Syst. 12 (2005), 347354.Google Scholar
Chen, W., Li, C. and Ou, B., ‘Classification of solutions for an integral equation’, Comm. Pure Appl. Math. 59 (2006), 330343.Google Scholar
Kilpelaiinen, T. and Maly, J., ‘The Wiener test and potential estimates for quasilinear elliptic equations’, Acta Math. 172 (1994), 137161.Google Scholar
Labutin, D., ‘Potential estimates for a class of fully nonlinear elliptic equations’, Duke Math. J. 111 (2002), 149.Google Scholar
Lei, Y., ‘Decay rates for solutions of an integral system of Wolff type’, Potential Anal. 35 (2011), 387402.Google Scholar
Lei, Y., ‘Qualitative properties of positive solutions of quasilinear equations with Hardy terms’, Forum Math. 29 (2017), 11771198.Google Scholar
Lei, Y. and Li, C., ‘Integrability and asymptotics of positive solutions of a 𝛾-Laplace system’, J. Differential Equations 252 (2012), 27392758.Google Scholar
Lei, Y. and Li, C., ‘Sharp criteria of Liouville type for some nonlinear systems’, Discrete Contin. Dyn. Syst. 36 (2016), 32773315.Google Scholar
Liu, S., ‘Regularity, symmetry, and uniqueness of some integral type quasilinear equations’, Nonlinear Anal. 71 (2009), 17961806.Google Scholar
Ma, C., Chen, W. and Li, C., ‘Regularity of solutions for an integral system of Wolff type’, Adv. Math. 226 (2011), 26762699.10.1016/j.aim.2010.07.020Google Scholar
Phuc, N. and Verbitsky, I., ‘Quasilinear and Hessian equations of Lane-Emden type’, Ann. of Math. (2) 168 (2008), 859914.Google Scholar
Villavert, J., ‘A characterization of fast decaying solutions for quasilinear and Wolff type systems with singular coefficients’, J. Math. Anal. Appl. 424 (2015), 13481373.Google Scholar
Villavert, J., ‘Asymptotic and optimal Liouville properties for Wolff type integral systems’, Nonlinear Anal. 130 (2016), 102120.10.1016/j.na.2015.09.017Google Scholar