On the de Thélin eigenvalue problem and Landesman-Lazer conditions for quasilinear systems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916019262455808 |
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| author | Arcoya, David Borgia, Natalino Cingolani, Silvia |
| author_facet | Arcoya, David Borgia, Natalino Cingolani, Silvia |
| contents | In this paper we prove that the smallest eigenvalue $λ_1$ of the eigenvalue problem for a quasilinear elliptic systems introduced by de Thélin in \cite{DT}, is not only simple (in a suitable sense), but also isolated.
Moreover, we characterize variationally a sequence $\{λ_k\}_k$ of eigenvalues, taking into account a suitable deformation lemma for $C^1$ submanifolds proved in \cite{BON}. Furthermore we prove the existence of a weak solution for a quasilinear elliptic systems in resonance around $λ_1$, under new sufficient Landesman-Lazer type conditions, extending the results by Arcoya and Orsina \cite{AO}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16846 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the de Thélin eigenvalue problem and Landesman-Lazer conditions for quasilinear systems Arcoya, David Borgia, Natalino Cingolani, Silvia Analysis of PDEs 35B34, 35J62, 35J92, 47J30, 58E05 In this paper we prove that the smallest eigenvalue $λ_1$ of the eigenvalue problem for a quasilinear elliptic systems introduced by de Thélin in \cite{DT}, is not only simple (in a suitable sense), but also isolated. Moreover, we characterize variationally a sequence $\{λ_k\}_k$ of eigenvalues, taking into account a suitable deformation lemma for $C^1$ submanifolds proved in \cite{BON}. Furthermore we prove the existence of a weak solution for a quasilinear elliptic systems in resonance around $λ_1$, under new sufficient Landesman-Lazer type conditions, extending the results by Arcoya and Orsina \cite{AO}. |
| title | On the de Thélin eigenvalue problem and Landesman-Lazer conditions for quasilinear systems |
| topic | Analysis of PDEs 35B34, 35J62, 35J92, 47J30, 58E05 |
| url | https://arxiv.org/abs/2601.16846 |