Normalized solutions to an exponential growth Choquard equation driven by mixed local-nonlocal operator in ℝ²

@misc{nidhi2026normalized,
  title = {{Normalized solutions to an exponential growth Choquard equation driven by mixed local-nonlocal operator in $\mathbbR^2$}},
  author = {Nidhi Nidhi and L. Sharma and K. Sreenadh},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.02141},
  eprint = {2606.02141},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.02141},
}

TY  - UNPB
TI  - Normalized solutions to an exponential growth Choquard equation driven by mixed local-nonlocal operator in ℝ^2
AU  - Nidhi Nidhi
AU  - L. Sharma
AU  - K. Sreenadh
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2606.02141
UR  - https://arxiv.org/abs/2606.02141
AB  - In this paper, we study the existence of normalized solutions to the mixed nonlinear Choquard equation with exponential growth { ℒu+λu = Λ(I_α*F(u))f(u) in ℝ^2; ∫_ℝ^2|u|^2 dx = a^2, . where ℒ=−Δ+(−Δ)^s, 0<s<1, a>0, I_α is the Riesz potential of order α∈(0,2), Λ>0, and λ∈ℝ arises as a Lagrange multiplier. The nonlinearity has critical exponential growth in the sense of the Trudinger-Moser inequality. Using variational methods, the associated Pohožaev manifold, and suitable Moser-type estimates, we establish the existence of a normalized solution of mountain-pass type with associated non zero Lagrange multiplier. Under an additional monotonicity assumption on the nonlinearity, we further show that the obtained solution is a normalized ground state. We also establish the regularity properties required for the proof of the corresponding Pohožaev identity.
ER  -