On singularly perturbed $(p, N )$-Laplace Schrödinger equation with logarithmic nonlinearity
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917030866714624 |
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| author | Mahanta, Deepak Kumar Mukherjee, Tuhina Winkert, Patrick |
| author_facet | Mahanta, Deepak Kumar Mukherjee, Tuhina Winkert, Patrick |
| contents | This article focuses on the study of the existence, multiplicity and concentration behavior of ground states as well as the qualitative aspects of positive solutions for a $(p, N)$-Laplace Schrödinger equation with logarithmic nonlinearity and critical exponential nonlinearity in the sense of Trudinger-Moser in the whole Euclidean space $\mathbb{R}^N$. Through the use of smooth variational methods, penalization techniques, and the application of the Lusternik-Schnirelmann category theory, we establish a connection between the number of positive solutions and the topological properties of the set in which the potential function achieves its minimum values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03788 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On singularly perturbed $(p, N )$-Laplace Schrödinger equation with logarithmic nonlinearity Mahanta, Deepak Kumar Mukherjee, Tuhina Winkert, Patrick Analysis of PDEs 35A15, 35D30, 35J10, 35J60, 35J92 This article focuses on the study of the existence, multiplicity and concentration behavior of ground states as well as the qualitative aspects of positive solutions for a $(p, N)$-Laplace Schrödinger equation with logarithmic nonlinearity and critical exponential nonlinearity in the sense of Trudinger-Moser in the whole Euclidean space $\mathbb{R}^N$. Through the use of smooth variational methods, penalization techniques, and the application of the Lusternik-Schnirelmann category theory, we establish a connection between the number of positive solutions and the topological properties of the set in which the potential function achieves its minimum values. |
| title | On singularly perturbed $(p, N )$-Laplace Schrödinger equation with logarithmic nonlinearity |
| topic | Analysis of PDEs 35A15, 35D30, 35J10, 35J60, 35J92 |
| url | https://arxiv.org/abs/2408.03788 |