Ground state sign-changing solutions for the Chern-Simons-Schrödinger equation with zero mass potential
نویسندگان
چکیده
This paper is concerned with the following nonlinear Chern-Simons-Schrödinger equation zero mass potential $ \begin{align} -\Delta u+\lambda\left(\frac{h_u^2(|x|)}{|x|^2}+\int^{\infty}_{|x|}\frac{h_u(s)}{s}u^2(s)ds\right)u = -a|u|^{p-2}u+f(u),\ \ x\in\mathbb{R}^2, \end{align} where a, \lambda>0 $, p\in (2,3) and$ h_u(s) \int^s_0\frac{\tau}{2}u^2(\tau)d\tau \frac{1}{4\pi}\int_{B_s}u^2(x)dx $is so-called Chern-Simons term, f has subcritical exponential growth in sense of Trudinger-Moser. Under some wild assumptions on combining Trudinger-Moser inequality, Non-Nehari manifold method and constraint minimization argument, we establish existence a ground state sign-changing solution u_{\lambda} for above equation, corresponding energy strictly larger than twice that solutions Nehari-type. Moreover, obtain convergence property as parameter \lambda \searrow 0 $. Our theorems extend results Xie Chen [Appl. Anal., 99 (2020), 880-898], Kang, Li Tang [Bull. Malays. Math. Sci. Soc., 44 (2021), 711-731] Shen [Complex Var. Elliptic Equ., 67 (2022), 1186-1203].
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems - Series S
سال: 2023
ISSN: ['1937-1632', '1937-1179']
DOI: https://doi.org/10.3934/dcdss.2023137