We consider the N-Laplacian Schrödinger equation strongly coupled with higher order fractional Poisson's equations. When the order of the Riesz potential α is equal to the Euclidean dimension N, and thus it is a logarithm, the system turns out to be equivalent to a nonlocal Choquard type equation. On the one hand, the natural function space setting in which the Schrödinger energy is well defined is the Sobolev limiting space W1,N(RN), where the maximal nonlinear growth is of exponential type. On the other hand, in order to have the nonlocal energy well defined and prove the existence of finite energy solutions, we introduce a suitable log-weighted variant of the Pohozaev-Trudinger inequality which provides a suitable functional framework where we use variational methods.

Quasilinear logarithmic Choquard equations with exponential growth in RN / C. Bucur, D. Cassani, C. Tarsi. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 328(2022 Aug 15), pp. 261-294. [10.1016/j.jde.2022.05.002]

Quasilinear logarithmic Choquard equations with exponential growth in RN

C. Bucur
Primo
;
C. Tarsi
Ultimo
2022-08-15

Abstract

We consider the N-Laplacian Schrödinger equation strongly coupled with higher order fractional Poisson's equations. When the order of the Riesz potential α is equal to the Euclidean dimension N, and thus it is a logarithm, the system turns out to be equivalent to a nonlocal Choquard type equation. On the one hand, the natural function space setting in which the Schrödinger energy is well defined is the Sobolev limiting space W1,N(RN), where the maximal nonlinear growth is of exponential type. On the other hand, in order to have the nonlocal energy well defined and prove the existence of finite energy solutions, we introduce a suitable log-weighted variant of the Pohozaev-Trudinger inequality which provides a suitable functional framework where we use variational methods.
Higher order fractional Schrödinger-Poisson systems; Schrödinger-Newton equations; Nonlocal nonlinear elliptic equations; Weighted Trudinger-Moser type inequalities in RN; Variational methods;
Settore MAT/05 - Analisi Matematica
Article (author)
File in questo prodotto:
File Dimensione Formato  
BCTArXIV.pdf

accesso aperto

Tipologia: Pre-print (manoscritto inviato all'editore)
Dimensione 320.84 kB
Formato Adobe PDF
320.84 kB Adobe PDF Visualizza/Apri
1-s2.0-S002203962200300X-main.pdf

solo utenti autorizzati

Tipologia: Publisher's version/PDF
Dimensione 405.49 kB
Formato Adobe PDF
405.49 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/929406
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? ND
social impact