Normalized solutions to a critical growth Choquard equation involving mixed operators

Article type: Research Article

Authors: Giacomoni, J.^{a; *} | Nidhi, Nidhi^b | Sreenadh, K.^b

Affiliations: [a] LMAP (UMR E2S UPPA CNRS 5142) Bat. IPRA, Avenue de l’Université, 64013 Pau, France | [b] Department of Mathematics, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi-110016, India

Correspondence: [*] Corresponding author. E-mail: jacques.giacomoni@univ-pau.fr.

Abstract: In this paper we study the existence and regularity results of normalized solutions to the following critical growth Choquard equation with mixed diffusion type operators: −Δu+(−Δ)su=λu+g(u)+(Iα∗|u|2α∗)|u|2α∗−2uin RN,∫RN|u|2dx=τ2, where N⩾3, τ>0, Iα is the Riesz potential of order α∈(0,N), (−Δ)s is the fractional laplacian operator, 2α∗=N+αN−2 is the critical exponent with respect to the Hardy Littlewood Sobolev inequality, λ appears as a Lagrange multiplier and g is a real valued function satisfying some L2-supercritical conditions.

Keywords: Normalized solutions, Choquard equation, critical growth, local and nonlocal operator, L²-supercritical growth, existence results, Sobolev regularity

DOI: 10.3233/ASY-241933

Journal: Asymptotic Analysis, vol. Pre-press, no. Pre-press, pp. 1-34, 2024