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arXiv · 2310.08460

Schr\"odinger-Poisson systems with zero mass in the Sobolev limiting case

Giulio Romani
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Abstract

We study the existence of positive solutions for a class of systems which strongly couple a quasilinear Schr\"odinger 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.

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Giulio Romani. 2023-10-12. Schr\"odinger-Poisson systems with zero mass in the Sobolev limiting case. https://doi.org/10.1002/mana.202300514

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