Generalized Chern-Simons-Schrodinger system with critical exponential growth: the zero mass case
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929291047993344 |
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| author | Shen, Liejun Squassina, Marco |
| author_facet | Shen, Liejun Squassina, Marco |
| contents | We consider the existence of ground state solutions for a class of zero-mass Chern-Simons-Schrödinger systems \[
\left\{
\begin{array}{ll} \displaystyle -Δu +A_0 u+\sum\limits_{j=1}^2A_j^2 u=f(u)-a(x)|u|^{p-2}u, \newline
\displaystyle \partial_1A_2-\partial_2A_1=-\frac{1}{2}|u|^2,~\partial_1A_1+\partial_2A_2=0, \newline
\displaystyle \partial_1A_0=A_2|u|^2,~ \partial_2A_0=-A_1|u|^2,
\end{array} \right. \] where $a:\mathbb R^2\to\mathbb R^+$ is an external potential, $p\in(1,2)$ and $f\in \mathcal{C}(\mathbb R)$ denotes a nonlinearity that fulfills the critical exponential growth in the Trudinger-Moser sense at infinity. By introducing an improvement of the version of Trudinger-Moser inequality, we are able to investigate the existence of positive ground state solutions for the given system using variational method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Chern-Simons-Schrodinger system with critical exponential growth: the zero mass case Shen, Liejun Squassina, Marco Analysis of PDEs 35J20, 58E50, 35B06 We consider the existence of ground state solutions for a class of zero-mass Chern-Simons-Schrödinger systems \[ \left\{ \begin{array}{ll} \displaystyle -Δu +A_0 u+\sum\limits_{j=1}^2A_j^2 u=f(u)-a(x)|u|^{p-2}u, \newline \displaystyle \partial_1A_2-\partial_2A_1=-\frac{1}{2}|u|^2,~\partial_1A_1+\partial_2A_2=0, \newline \displaystyle \partial_1A_0=A_2|u|^2,~ \partial_2A_0=-A_1|u|^2, \end{array} \right. \] where $a:\mathbb R^2\to\mathbb R^+$ is an external potential, $p\in(1,2)$ and $f\in \mathcal{C}(\mathbb R)$ denotes a nonlinearity that fulfills the critical exponential growth in the Trudinger-Moser sense at infinity. By introducing an improvement of the version of Trudinger-Moser inequality, we are able to investigate the existence of positive ground state solutions for the given system using variational method. |
| title | Generalized Chern-Simons-Schrodinger system with critical exponential growth: the zero mass case |
| topic | Analysis of PDEs 35J20, 58E50, 35B06 |
| url | https://arxiv.org/abs/2403.18014 |