TY - JOUR
T1 - Multiple Sign-Changing Solutions for Quasilinear Equations of Bounded Quasilinearity
AU - Liu , Jiaquan
AU - Liu , Xiangqing
AU - Wang , Zhi-Qiang
JO - Analysis in Theory and Applications
VL - 2
SP - 209
EP - 229
PY - 2021
DA - 2021/04
SN - 37
DO - http://doi.org/10.4208/ata.2021.pr80.02
UR - https://global-sci.org/intro/article_detail/ata/18772.html
KW - Quasilinear elliptic equations, sign-changing solution, an elliptic regularization method.
AB - <p style="text-align: justify;">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</p><p style="text-align:center"><img src="https://admin.global-sci.org/uploads/ueditor/image/20210419/1618806160701482.jpg" title="1618806160701482.jpg" alt="a.JPG"/></p><p style="text-align: justify;">where $\Omega\subset\mathbb{R}^N$ is a bounded domain with smooth boundary, and we use<br/></p><p style="text-align:center"><img src="https://admin.global-sci.org/uploads/ueditor/image/20210419/1618806215853944.jpg" title="1618806215853944.jpg" alt="b.JPG"/></p><p style="text-align: justify;">The main interest of this paper is for the case of bounded quasilinearity $b_{ij}$. The result is proved by an elliptic regularization method involving truncations of both $u$ and the gradient of $u$.</p>