On Bobkov-Tanaka type spectrum for the double-phase operator
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908291039232000 |
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| author | Gambera, Laura Guarnotta, Umberto |
| author_facet | Gambera, Laura Guarnotta, Umberto |
| contents | Moving from the seminal papers by Bobkov and Tanaka \cite{BT,BT2,BT3} on the spectrum of the $(p,q)$-Laplacian, we analyze the case of the double-phase operator. We discuss the region of parameters in which existence and non-existence of positive solutions occur. The proofs are based on normalization procedures, the Nehari manifold, and truncation techniques, exploiting Picone-type inequalities and an ad-hoc strong maximum principle. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_16147 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Bobkov-Tanaka type spectrum for the double-phase operator Gambera, Laura Guarnotta, Umberto Analysis of PDEs 35J60, 35J25, 35B38, 35P30 Moving from the seminal papers by Bobkov and Tanaka \cite{BT,BT2,BT3} on the spectrum of the $(p,q)$-Laplacian, we analyze the case of the double-phase operator. We discuss the region of parameters in which existence and non-existence of positive solutions occur. The proofs are based on normalization procedures, the Nehari manifold, and truncation techniques, exploiting Picone-type inequalities and an ad-hoc strong maximum principle. |
| title | On Bobkov-Tanaka type spectrum for the double-phase operator |
| topic | Analysis of PDEs 35J60, 35J25, 35B38, 35P30 |
| url | https://arxiv.org/abs/2405.16147 |