Abstract
In this paper, we consider the multiplicity of solutions to the following Choquard equation (Formula presented.) with a prescribed mass (Formula presented.) where N≥1, a,ε>0, α∈(0,N), N+αN<p<N+α+2N, Iα is the Riesz potential, λ∈R appears as an unknown Lagrange multiplier, h:RN→[0,∞) is a bounded and continuous function and the potential V is a continuous function. Under some assumptions on V, we show that when ε is small enough the numbers of normalized ground states are at least the numbers of global maximum points of h.
| Original language | English |
|---|---|
| Article number | 12 |
| Journal | Journal of Geometric Analysis |
| Volume | 35 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2025 |
| Externally published | Yes |
Keywords
- 35A15
- 35J15
- Choquard equations
- Multiplicity
- Normalized solutions
- Variational method
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Meng, Y., & Wang, B. (2025). Multiplicity of Normalized Solutions to a Class of Non-autonomous Choquard Equations. Journal of Geometric Analysis, 35(1), Article 12. https://doi.org/10.1007/s12220-024-01844-x