Existence of infinitely many solutions for the fractional Schrödinger- Maxwell equations
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2015
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917696627539968 |
|---|---|
| author | Wei, Zhongli |
| author_facet | Wei, Zhongli |
| contents | In this paper, by using variational methods and critical point theory, we shall mainly study the existence of infinitely many solutions for the following fractional Schrödinger-Maxwell equations $$( -Δ)^α u+V(x)u+ϕu=f(x,u), \hbox{in } \mathbb{R}^3 ,$$ $$ (-\triangle)^αϕ=K_α u^2 \ \ \mathrm{in}\ \ \mathbb{R}^3 $$ where $α\in (0,1],$ $K_α=\dfrac{π^{-α}Γ(α)}{π^{-(3-2α)/2}Γ((3-2α)/2)},$ $( -Δ)^α$ stands for the fractional Laplacian. Under some more assumptions on $f,$ we get infinitely many solutions for the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1508_03088 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Existence of infinitely many solutions for the fractional Schrödinger- Maxwell equations Wei, Zhongli Analysis of PDEs 35B40, 35B45, 35J55, 35J60, 47J30 In this paper, by using variational methods and critical point theory, we shall mainly study the existence of infinitely many solutions for the following fractional Schrödinger-Maxwell equations $$( -Δ)^α u+V(x)u+ϕu=f(x,u), \hbox{in } \mathbb{R}^3 ,$$ $$ (-\triangle)^αϕ=K_α u^2 \ \ \mathrm{in}\ \ \mathbb{R}^3 $$ where $α\in (0,1],$ $K_α=\dfrac{π^{-α}Γ(α)}{π^{-(3-2α)/2}Γ((3-2α)/2)},$ $( -Δ)^α$ stands for the fractional Laplacian. Under some more assumptions on $f,$ we get infinitely many solutions for the system. |
| title | Existence of infinitely many solutions for the fractional Schrödinger- Maxwell equations |
| topic | Analysis of PDEs 35B40, 35B45, 35J55, 35J60, 47J30 |
| url | https://arxiv.org/abs/1508.03088 |