TY - JOUR AU - Alves, Claudianor O. AU - Freitas, Luciana R. de PY - 2012/04/23 Y2 - 2024/03/28 TI - Multiplicity of nonradial solutions for a class of quasilinear equations on annulus with exponential critical growth JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 39 IS - 2 SE - DO - UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2012.014 SP - 243 - 262 AB - In this paper, we establish the existence of many rotationally non-equivalent and nonradial solutions for the following class of quasilinear problems $$\cases-\Delta_{N} u = \lambda f(|x|,u) &x\in \Omega_r,\\ u > 0 &x\in \Omega_r,\\ u=0 &x\in \partial\Omega_r,\endcases\tag P$$where $\Omega_r = \{ x \in \mathbb{R}^{N}: r < |x| < r+1\}$, $N \geq 2$, $N eq 3$, $r > 0$, $\lambda > 0$, $\Delta_{N}u= \div(| abla u|^{N-2} abla u ) $ is the $N$-Laplacian operator and $f$ is a continuous function with exponential critical growth. ER -