Multiple Sign-Changing Solutions for Quasilinear Equations of Bounded Quasilinearity

The existence of an infinite sequence of sign-changing solutions are proved for a class of quasilinear elliptic equations under suitable conditions on the quasilinear coefficients and the nonlinearity{N∑i,j=1 (bij(u)Diju+1/2Dzbij(u)DiuDju)+f(u)=0 in Ω,u =0 on (e)Ω,where Ω (c) RN is a bounded domain...

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Bibliographic Details
Published in:Analysis in theory & applications 2021-01, Vol.37 (2), p.209-229
Main Authors: Jiaquan Liu, Jiaquan Liu, Xiangqing Liu, Xiangqing Liu, Zhi-Qiang Wang, Zhi-Qiang Wang
Format: Article
Language:English
Online Access:Get full text
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Summary:The existence of an infinite sequence of sign-changing solutions are proved for a class of quasilinear elliptic equations under suitable conditions on the quasilinear coefficients and the nonlinearity{N∑i,j=1 (bij(u)Diju+1/2Dzbij(u)DiuDju)+f(u)=0 in Ω,u =0 on (e)Ω,where Ω (c) RN is a bounded domain with smooth boundary,and we use Diu =(e)u/(e)xi,Diju=(e)2u/(e)xi(e)xj,and Dzbij(z) =d/dzbij(z).The main interest of this paper is for the case of bounded quasilinearity bij.The result is proved by an elliptic regularization method involving truncations of both u and the gradient of u.
ISSN:1672-4070
1573-8175
DOI:10.4208/ata.2021.pr80.02