Existence of solution for two classes of Schrödinger equations in $\mathbb{R}^N$ with magnetic field and zero mass
In this paper, we consider the existence of a nontrivial solution for the following Schrödinger equations with a magnetic potential $A$ $$-\Delta_A u=K(x)f(|u|^2)u,~\quad \mbox{in}~\mathbb{R}^N$$ where $N\geqslant3$, $K$ is a nonnegative function verifying two kinds of conditions and $f$ is continuo...
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University of Szeged
2020-01-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7983 |
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doaj-4599e15387c94990bedb8090c5b301b12021-07-14T07:21:33ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751417-38752020-01-012020711610.14232/ejqtde.2020.1.77983Existence of solution for two classes of Schrödinger equations in $\mathbb{R}^N$ with magnetic field and zero massZhao Yin0Chao Ji1Department of Mathematics, East China University of Science and Technology, Shanghai, P.R. ChinaDepartment of Mathematics, East China University of Science and Technology, Shanghai, P.R. ChinaIn this paper, we consider the existence of a nontrivial solution for the following Schrödinger equations with a magnetic potential $A$ $$-\Delta_A u=K(x)f(|u|^2)u,~\quad \mbox{in}~\mathbb{R}^N$$ where $N\geqslant3$, $K$ is a nonnegative function verifying two kinds of conditions and $f$ is continuous with subcritical growth.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7983schrödinger equationmagnetic fieldzero massperiodic conditionasymptotically periodic condition |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Zhao Yin Chao Ji |
| spellingShingle |
Zhao Yin Chao Ji Existence of solution for two classes of Schrödinger equations in $\mathbb{R}^N$ with magnetic field and zero mass Electronic Journal of Qualitative Theory of Differential Equations schrödinger equation magnetic field zero mass periodic condition asymptotically periodic condition |
| author_facet |
Zhao Yin Chao Ji |
| author_sort |
Zhao Yin |
| title |
Existence of solution for two classes of Schrödinger equations in $\mathbb{R}^N$ with magnetic field and zero mass |
| title_short |
Existence of solution for two classes of Schrödinger equations in $\mathbb{R}^N$ with magnetic field and zero mass |
| title_full |
Existence of solution for two classes of Schrödinger equations in $\mathbb{R}^N$ with magnetic field and zero mass |
| title_fullStr |
Existence of solution for two classes of Schrödinger equations in $\mathbb{R}^N$ with magnetic field and zero mass |
| title_full_unstemmed |
Existence of solution for two classes of Schrödinger equations in $\mathbb{R}^N$ with magnetic field and zero mass |
| title_sort |
existence of solution for two classes of schrödinger equations in $\mathbb{r}^n$ with magnetic field and zero mass |
| publisher |
University of Szeged |
| series |
Electronic Journal of Qualitative Theory of Differential Equations |
| issn |
1417-3875 1417-3875 |
| publishDate |
2020-01-01 |
| description |
In this paper, we consider the existence of a nontrivial solution for the following Schrödinger equations with a magnetic potential $A$
$$-\Delta_A u=K(x)f(|u|^2)u,~\quad \mbox{in}~\mathbb{R}^N$$
where $N\geqslant3$, $K$ is a nonnegative function verifying two kinds of conditions and $f$ is continuous with subcritical growth. |
| topic |
schrödinger equation magnetic field zero mass periodic condition asymptotically periodic condition |
| url |
http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7983 |
| work_keys_str_mv |
AT zhaoyin existenceofsolutionfortwoclassesofschrodingerequationsinmathbbrnwithmagneticfieldandzeromass AT chaoji existenceofsolutionfortwoclassesofschrodingerequationsinmathbbrnwithmagneticfieldandzeromass |
| _version_ |
1721303346614108160 |