Ground state radial sign-changing solutions for a gauged nonlinear Schrödinger equation involving critical growth
Ground state radial sign-changing solutions for a gauged nonlinear Schrödinger equation involving critical growth
We investigate the following gauged nonlinear Schrödinger equation $ \begin{equation*} \begin{cases} -\Delta u+\omega u+\lambda\bigg(\dfrac{h_{u}^{2}(|x|)}{|x|^{2}}+ \int_{|x|}^{+\infty}\dfrac{h_{u}(s)}{s}u^{2}(s)ds\bigg)u = f(u) \ \ \ \ \ \mbox{in}\ \mathbb{R}^{2},\\ u\in H_r^1(\mathbb{R}^{2}), \end{cases} \end{equation*} $ where $ \omega,\lambda>0 $ and $ h_{u}(s) = \frac{1}{2}\int_{0}^{s}ru^{2}(r)dr $. When $ f $ has exponential critical growth, by using the …