TY  - JOUR
ID  - Nidhi2026
LB  - Nidhi2026
AU  - Nidhi, Nidhi
AU  - Sreenadh, Konijeti
TI  - Solutions with prescribed mass for a critical Choquard equation driven by a local-nonlocal operator
ST  - Solutions with prescribed mass for a critical Choquard equation driven by a local-nonlocal operator
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2026
VL  - 46
IS  - 2
SP  - 235
EP  - 266
DO  - https://doi.org/10.7494/OpMath.202603181
UR  - https://doi.org/10.7494/OpMath.202603181
AB  - 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 \(\tau\).
KW  - normalized solution
KW  - Choquard equation
KW  - critical exponent
KW  - mixed local and nonlocal operator
KW  - \(L^2\)-subcritical perturbation
KW  - nonlinear Schrödinger equation driven by local-nonlocal operator
SN  - 1232-9274
ER  -