@Article{Nidhi2026,
author = "Nidhi, Nidhi and Sreenadh, Konijeti",
title = "Solutions with prescribed mass for a critical Choquard equation driven by a local-nonlocal operator",
journal = "Opuscula Math.",
year = "2026",
volume = "46",
number = "2",
pages = "235--266",
doi = "https://doi.org/10.7494/OpMath.202603181",
url = "https://doi.org/10.7494/OpMath.202603181",
abstract = "In this paper, we study the normalized solutions of the following critical growth Choquard equation with mixed local and nonlocal operators: \[\begin{split}-\Delta u +(-\Delta)^s u &= \lambda u +\mu |u|^{p-2}u +(I_{\alpha}*|u|^{2^*_{\alpha}})|u|^{2^*_{\alpha}-2}u \quad\text{in}\quad \mathbb{R}^N,\\ \| u\|_2 &= \tau,\end{split}\] where \(N\geq 3\), \(\tau\gt 0\), \(I_{\alpha}\) is the Riesz potential of order \(\alpha\in (0,N)\), \(2^*_{\alpha}=\frac{N+\alpha}{N-2}\) is the critical exponent corresponding to the Hardy-Littlewood-Sobolev inequality, \((-\Delta)^s\) is the nonlocal fractional Laplacian operator with \(s\in (0,1)\), \(\mu\gt 0\) is a parameter and \(\lambda\) appears as Lagrange multiplier. We show the existence of at least two distinct solutions in the presence of the mass-subcritical perturbation \(\mu |u|^{p-2}u\) with \(2\gt p\gt 2+\frac{4s}{N}\) under some assumptions on \(\tau\).",
keywords = "normalized solution, Choquard equation, critical exponent, mixed local and nonlocal operator, \(L^2\)-subcritical perturbation, nonlinear Schrödinger equation driven by local-nonlocal operator",
issn = "1232-9274"
}