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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2025-05-01
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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=11366 |
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| Summary: | 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. |
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| ISSN: | 1417-3875 |