In this paper we consider the problem(P lambda()) {-Delta u + V-lambda(x)u = (I-mu * vertical bar u vertical bar(2 mu*))vertical bar u vertical bar(2 mu*-2)u in R-N,u > 0 in R-N,where V-lambda = lambda + V-0 with lambda >= 0, V-0 is an element of L-N/2(R-N), I-mu = 1/vertical bar x vertical bar(mu) is the Riesz potential with 0 < mu < min{N, 4} and 2(mu)* = 2N-mu/N-2 with N >= 3. Under some smallness assumption on V-0 and lambda we prove the existence of two positive solutions of (P-lambda). In order to prove the main results, we used variational methods combined with degree theory.

Alves, C., Figueiredo, G., Molle, R. (2021). Multiple positive bound state solutions for a critical Choquard equation. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 41(10), 4887-4919 [10.3934/dcds.2021061].

Multiple positive bound state solutions for a critical Choquard equation

Molle, R
2021-01-01

Abstract

In this paper we consider the problem(P lambda()) {-Delta u + V-lambda(x)u = (I-mu * vertical bar u vertical bar(2 mu*))vertical bar u vertical bar(2 mu*-2)u in R-N,u > 0 in R-N,where V-lambda = lambda + V-0 with lambda >= 0, V-0 is an element of L-N/2(R-N), I-mu = 1/vertical bar x vertical bar(mu) is the Riesz potential with 0 < mu < min{N, 4} and 2(mu)* = 2N-mu/N-2 with N >= 3. Under some smallness assumption on V-0 and lambda we prove the existence of two positive solutions of (P-lambda). In order to prove the main results, we used variational methods combined with degree theory.
2021
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Choquard equation
Variational methods
Critical exponents
C.O. Alves is partially supported by CNPq/Brazil 304804/ 2017-7. G. M. Figueiredo is supported by CNPq and FAPDF. R. Molle is supported by the MIUR Excellence Department Project CUP E83C18000100006 (Roma Tor Vergata University) and by the INdAM-GNAMPA group.
Alves, C., Figueiredo, G., Molle, R. (2021). Multiple positive bound state solutions for a critical Choquard equation. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 41(10), 4887-4919 [10.3934/dcds.2021061].
Alves, C; Figueiredo, G; Molle, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/285263
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