| Autor: |
Deng Yinbin, Liu Chenchen, Yang Xian |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Advances in Nonlinear Analysis, Vol 13, Iss 1, Pp 30-276 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2191-950X |
| DOI: |
10.1515/anona-2024-0055 |
| Popis: |
This study deals with the existence of nodal solutions for the following gauged nonlinear Schrödinger equation with zero mass: −Δu+hu2(∣x∣)∣x∣2+∫∣x∣+∞hu(s)su2(s)dsu=∣u∣p−2u,x∈R2,-\Delta u+\left(\frac{{h}_{u}^{2}\left(| x| )}{{| x| }^{2}}+\underset{| x| }{\overset{+\infty }{\int }}\frac{{h}_{u}\left(s)}{s}{u}^{2}\left(s){\rm{d}}s\right)u={| u| }^{p-2}u,\hspace{1.0em}x\in {{\mathbb{R}}}^{2}, where p>6p\gt 6 and hu(s)=12∫0sru2(r)dr{h}_{u}\left(s)=\frac{1}{2}{\int }_{0}^{s}r{u}^{2}\left(r){\rm{d}}r. By variational methods, we prove that for any integer k≥0k\ge 0, the above equation has a nodal solution wk{w}_{k} which changes sign exactly kk times. Moreover, we also prove that wk{w}_{k} belongs to L2(R2){L}^{2}\left({{\mathbb{R}}}^{2}) provided p>10p\gt 10. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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