Schrödinger-Poisson systems with zero mass in the Sobolev limiting case
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913953372700672 |
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| author | Romani, Giulio |
| author_facet | Romani, Giulio |
| contents | We study the existence of positive solutions for a class of systems which strongly couple a quasilinear Schrödinger equation driven by a weighted $N$-Laplace operator and without the mass term, and a higher-order fractional Poisson equation. Since the system is considered in $\mathbb R^N$, the limiting case for the Sobolev embedding, we consider nonlinearities with exponential growth. Existence is proved relying on the study of a corresponding Choquard equation in which the Riesz kernel is a sign-changing logarithm. This is in turn solved by means of a variational approximating procedure for an auxiliary Choquard equation where the logarithm is uniformly approximated by polynomial kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08460 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Schrödinger-Poisson systems with zero mass in the Sobolev limiting case Romani, Giulio Analysis of PDEs 35A15, 35J50, 35J60, 35Q55 We study the existence of positive solutions for a class of systems which strongly couple a quasilinear Schrödinger equation driven by a weighted $N$-Laplace operator and without the mass term, and a higher-order fractional Poisson equation. Since the system is considered in $\mathbb R^N$, the limiting case for the Sobolev embedding, we consider nonlinearities with exponential growth. Existence is proved relying on the study of a corresponding Choquard equation in which the Riesz kernel is a sign-changing logarithm. This is in turn solved by means of a variational approximating procedure for an auxiliary Choquard equation where the logarithm is uniformly approximated by polynomial kernels. |
| title | Schrödinger-Poisson systems with zero mass in the Sobolev limiting case |
| topic | Analysis of PDEs 35A15, 35J50, 35J60, 35Q55 |
| url | https://arxiv.org/abs/2310.08460 |