Affiliation:
1. Dipartimento di Scienza e Alta Tecnologia Università degli Studi dell'Insubria Varese Italy
2. RISM‐Riemann International School of Mathematics Varese Italy
Abstract
AbstractWe study the existence of positive solutions for a class of systems which strongly couple a quasilinear Schrödinger equation driven by a weighted ‐Laplace operator and without the mass term, and a higher‐order fractional Poisson equation. Since the system is set in , 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 logarithm, hence sign‐changing and unbounded from above and below. 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. Our results are new even in the planar case .
Funder
Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
Cited by
1 articles.
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