Existence and nonexistence of solutions for generalized quasilinear Kirchhoff–Schrödinger–Poisson system
In this paper, we consider the existence and nonexistence of solutions for a class of modified Schrödinger–Poisson system with Kirchhoff-type perturbation by use of variational methods. When nonlinear term $h(u)=|u|^{p-2}u$, $1\leq p<\infty$, the nonexistence of nontrivial solutions of system is...
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University of Szeged
2025-05-01
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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=11366 |
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| author | Yaru Wang Jing Zhang |
| author_facet | Yaru Wang Jing Zhang |
| author_sort | Yaru Wang |
| collection | DOAJ |
| description | In this paper, we consider the existence and nonexistence of solutions for a class of modified Schrödinger–Poisson system with Kirchhoff-type perturbation by use of variational methods. When nonlinear term $h(u)=|u|^{p-2}u$, $1\leq p<\infty$, the nonexistence of nontrivial solutions of system is demonstrated through Pohožaev identity. When nonlinear term $h(u)$ satisfies appropriate assumptions, taking advantage of critical point theorem, we obtain a positive radial solution and a nontrivial one of system when $g(u)$ satisfies different conditions. Moreover, some convergence properties are established as the parameter $b\rightarrow0$. What is more, the nonexistence of nontrivial solutions in critical case is also proved by use of Pohožaev identity. |
| format | Article |
| id | doaj-art-a25b20b7d76743f8a4bbb71bbd46cb03 |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-a25b20b7d76743f8a4bbb71bbd46cb032025-08-20T03:50:53ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752025-05-0120252512210.14232/ejqtde.2025.1.2511366Existence and nonexistence of solutions for generalized quasilinear Kirchhoff–Schrödinger–Poisson systemYaru Wang0Jing Zhanghttps://orcid.org/0000-0003-2599-1325Inner Mongolia Normal University, Hohhot, P.R. ChinaIn this paper, we consider the existence and nonexistence of solutions for a class of modified Schrödinger–Poisson system with Kirchhoff-type perturbation by use of variational methods. When nonlinear term $h(u)=|u|^{p-2}u$, $1\leq p<\infty$, the nonexistence of nontrivial solutions of system is demonstrated through Pohožaev identity. When nonlinear term $h(u)$ satisfies appropriate assumptions, taking advantage of critical point theorem, we obtain a positive radial solution and a nontrivial one of system when $g(u)$ satisfies different conditions. Moreover, some convergence properties are established as the parameter $b\rightarrow0$. What is more, the nonexistence of nontrivial solutions in critical case is also proved by use of Pohožaev identity.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11366variational methodspohožaev identitycritical point theoremnonexistenceradial solution |
| spellingShingle | Yaru Wang Jing Zhang Existence and nonexistence of solutions for generalized quasilinear Kirchhoff–Schrödinger–Poisson system Electronic Journal of Qualitative Theory of Differential Equations variational methods pohožaev identity critical point theorem nonexistence radial solution |
| title | Existence and nonexistence of solutions for generalized quasilinear Kirchhoff–Schrödinger–Poisson system |
| title_full | Existence and nonexistence of solutions for generalized quasilinear Kirchhoff–Schrödinger–Poisson system |
| title_fullStr | Existence and nonexistence of solutions for generalized quasilinear Kirchhoff–Schrödinger–Poisson system |
| title_full_unstemmed | Existence and nonexistence of solutions for generalized quasilinear Kirchhoff–Schrödinger–Poisson system |
| title_short | Existence and nonexistence of solutions for generalized quasilinear Kirchhoff–Schrödinger–Poisson system |
| title_sort | existence and nonexistence of solutions for generalized quasilinear kirchhoff schrodinger poisson system |
| topic | variational methods pohožaev identity critical point theorem nonexistence radial solution |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11366 |
| work_keys_str_mv | AT yaruwang existenceandnonexistenceofsolutionsforgeneralizedquasilinearkirchhoffschrodingerpoissonsystem AT jingzhang existenceandnonexistenceofsolutionsforgeneralizedquasilinearkirchhoffschrodingerpoissonsystem |