New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory
In this paper, we study the following quasilinear Schrödinger equation \begin{equation*} \begin{split} -\Delta u&+V(x)u-\kappa u\Delta(u^2)+\mu\frac{h^2(|x|)}{|x|^2}(1+\kappa u^2)u\\ &+\mu\left(\int_{|x|}^{+\infty}\frac{h(s)}{s}(2+\kappa u^2(s))u^2(s)\text{d}s\right)u=f(u)\quad\text{in}~\mat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2021-09-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9074 |
| Summary: | In this paper, we study the following quasilinear Schrödinger equation
\begin{equation*}
\begin{split}
-\Delta u&+V(x)u-\kappa u\Delta(u^2)+\mu\frac{h^2(|x|)}{|x|^2}(1+\kappa u^2)u\\
&+\mu\left(\int_{|x|}^{+\infty}\frac{h(s)}{s}(2+\kappa u^2(s))u^2(s)\text{d}s\right)u=f(u)\quad\text{in}~\mathbb{R}^2,
\end{split}
\end{equation*}
where $\kappa>0$, $\mu>0$, $V \in \mathcal{C}^1(\mathbb{R}^2,\mathbb{R})$ and $f \in \mathcal{C}(\mathbb{R},\mathbb{R})$. By using a constraint minimization of Pohožaev–Nehari type and analytic techniques, we obtain the existence of ground state solutions. |
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| ISSN: | 1417-3875 |