论文标题
非线性schrödinger-bopp-podolsky-proca系统的多个解决方案和配置文件描述
Multiple solutions and profile description for a nonlinear Schrödinger-Bopp-Podolsky-Proca system on a manifold
论文作者
论文摘要
我们证明了\ begin {equation*}的多重结果 \ begin {case} - \ \ varepsilon^{2}Δ_gu+oxu+q^{2} ϕu = | u |^{p-2} u \\ [1mm] -Δ_gϕ+ a^{2}δ_g^{2} ϕ+ m^2 ϕ =4πu^{2} \ end {cases} \ text {in} m，\ end {equation*}其中$（m，g）$是一种平滑而紧凑的$ 3 $二维的riemannian歧管，没有边界，$ p \ in（4,6）$，$ a，m，q \ neq neq 0 $，$ \ varepsilon> $ \ varepsilon> 0 $ afflofe此结果的证明依赖于Lusternik-Schnirellman类别。我们还为低能解决方案提供了个人资料描述。
We prove a multiplicity result for \begin{equation*} \begin{cases} -\varepsilon^{2}Δ_g u+ωu+q^{2}ϕu=|u|^{p-2}u\\[1mm] -Δ_g ϕ+a^{2}Δ_g^{2} ϕ+ m^2 ϕ=4πu^{2} \end{cases} \text{ in }M, \end{equation*} where $(M,g)$ is a smooth and compact $3$-dimensional Riemannian manifold without boundary, $p\in(4,6)$, $a,m,q\neq 0$, $\varepsilon>0$ small enough. The proof of this result relies on Lusternik-Schnirellman category. We also provide a profile description for low energy solutions.
