Infinitely many solutions for an instantaneous and non-instantaneous fourth-order differential system with local assumptions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909581495500800 |
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| author | Kang, Lijuan Zhang, Xingyong Liu, Cuiling |
| author_facet | Kang, Lijuan Zhang, Xingyong Liu, Cuiling |
| contents | We investigate a class of fourth-order differential systems with instantaneous and non-instantaneous impulses. Our technical approach is mainly based on a variant of Clark's theorem without the global assumptions. Under locally subquadratic growth conditions imposed on the nonlinear terms $f_i(t,u)$ and impulsive terms $I_i$, combined with perturbations governed by arbitrary continuous functions of small coefficient $\varepsilon$, we establish the existence of multiple small solutions. Specifically, the system exhibits infinitely many solutions in the case where $\varepsilon=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11738 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinitely many solutions for an instantaneous and non-instantaneous fourth-order differential system with local assumptions Kang, Lijuan Zhang, Xingyong Liu, Cuiling Analysis of PDEs We investigate a class of fourth-order differential systems with instantaneous and non-instantaneous impulses. Our technical approach is mainly based on a variant of Clark's theorem without the global assumptions. Under locally subquadratic growth conditions imposed on the nonlinear terms $f_i(t,u)$ and impulsive terms $I_i$, combined with perturbations governed by arbitrary continuous functions of small coefficient $\varepsilon$, we establish the existence of multiple small solutions. Specifically, the system exhibits infinitely many solutions in the case where $\varepsilon=0$. |
| title | Infinitely many solutions for an instantaneous and non-instantaneous fourth-order differential system with local assumptions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.11738 |