Normalized Solutions for the $(2,q)$-Laplacian Operator Between Mass-Critical Exponents
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911276433670144 |
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| author | Baldelli, Laura Ikoma, Norihisa |
| author_facet | Baldelli, Laura Ikoma, Norihisa |
| contents | This paper concerns the existence of normalized solutions to a class of $(2,q)$-Laplacian equations with a power type nonlinearity in the intermediate regime between the two mass critical exponents $2(1+2/N)$, $q(1+2/N)$. More precisely, we prove the existence of solutions with negative energy obtained through a global minimization procedure, and of solutions with positive energy established via a local minimization technique and a mountain-pass argument. Furthermore, we derive both existence and nonexistence results for the zero-mass case $λ= 0$, highlighting the role of the mixed diffusion in determining the qualitative behavior of solutions. Specifically, this paper's novelty lies in providing a comprehensive understanding of the intermediate cases that arise when the non-homogeneous $(2,q)$-Laplacian operator appears. Our analysis combines variational methods, compactness arguments, and delicate energy estimates adapted to the nonhomogeneous nature of the $(2,q)$-Laplacian operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normalized Solutions for the $(2,q)$-Laplacian Operator Between Mass-Critical Exponents Baldelli, Laura Ikoma, Norihisa Analysis of PDEs 35J20, 35J60, 35B38, 35A15 This paper concerns the existence of normalized solutions to a class of $(2,q)$-Laplacian equations with a power type nonlinearity in the intermediate regime between the two mass critical exponents $2(1+2/N)$, $q(1+2/N)$. More precisely, we prove the existence of solutions with negative energy obtained through a global minimization procedure, and of solutions with positive energy established via a local minimization technique and a mountain-pass argument. Furthermore, we derive both existence and nonexistence results for the zero-mass case $λ= 0$, highlighting the role of the mixed diffusion in determining the qualitative behavior of solutions. Specifically, this paper's novelty lies in providing a comprehensive understanding of the intermediate cases that arise when the non-homogeneous $(2,q)$-Laplacian operator appears. Our analysis combines variational methods, compactness arguments, and delicate energy estimates adapted to the nonhomogeneous nature of the $(2,q)$-Laplacian operator. |
| title | Normalized Solutions for the $(2,q)$-Laplacian Operator Between Mass-Critical Exponents |
| topic | Analysis of PDEs 35J20, 35J60, 35B38, 35A15 |
| url | https://arxiv.org/abs/2511.15285 |