Existence of multiple normalized solutions to a critical growth Choquard equation involving mixed operator
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914070431531008 |
|---|---|
| author | Nidhi, Nidhi Sreenadh, K. |
| author_facet | Nidhi, Nidhi Sreenadh, K. |
| contents | In this paper we study the normalized solutions of the following critical growth Choquard equation with mixed local and non-local operators:
\begin{equation*}
\begin{array}{rcl}
-Δu +(-Δ)^s u & = & λu +μ|u|^{p-2}u +(I_α*|u|^{2^*_α})|u|^{2^*_α-2}u \text{ in } \mathbb{R}^N;\;\;
\left\| u \right\|_2 & = & τ,
\end{array}
\end{equation*}
here $N\geq 3$, $τ>0$, $I_α$ is the Riesz potential of order $α\in (0,N)$, $2^*_α=\frac{N+α}{N-2}$ is the critical exponent corresponding to the Hardy Littlewood Sobolev inequality, $(-Δ)^s$ is the non-local fractional Laplacian operator with $s\in (0,1)$, $μ>0$ is a parameter and $λ$ appears as Lagrange multiplier. We have shown the existence of atleast two distinct solutions in the presence of mass subcritical perturbation, $μ|u|^{p-2}u$ with $2<p<2+\frac{4s}{N}$ under some assumptions on $τ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00893 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of multiple normalized solutions to a critical growth Choquard equation involving mixed operator Nidhi, Nidhi Sreenadh, K. Analysis of PDEs In this paper we study the normalized solutions of the following critical growth Choquard equation with mixed local and non-local operators: \begin{equation*} \begin{array}{rcl} -Δu +(-Δ)^s u & = & λu +μ|u|^{p-2}u +(I_α*|u|^{2^*_α})|u|^{2^*_α-2}u \text{ in } \mathbb{R}^N;\;\; \left\| u \right\|_2 & = & τ, \end{array} \end{equation*} here $N\geq 3$, $τ>0$, $I_α$ is the Riesz potential of order $α\in (0,N)$, $2^*_α=\frac{N+α}{N-2}$ is the critical exponent corresponding to the Hardy Littlewood Sobolev inequality, $(-Δ)^s$ is the non-local fractional Laplacian operator with $s\in (0,1)$, $μ>0$ is a parameter and $λ$ appears as Lagrange multiplier. We have shown the existence of atleast two distinct solutions in the presence of mass subcritical perturbation, $μ|u|^{p-2}u$ with $2<p<2+\frac{4s}{N}$ under some assumptions on $τ$. |
| title | Existence of multiple normalized solutions to a critical growth Choquard equation involving mixed operator |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.00893 |