论文标题
紧凑的Riemannian歧管上的frational p-Laplacian
Frational p-Laplacian on Compact Riemannian Manifold
论文作者
论文摘要
在本文中，我们调查了一类非局部方程的非平凡解决方案的存在和独特性，涉及分数$ p $ -laplacian操作员在紧凑型riemannian歧管上定义的，即 （-Δ_G）^s_p u（x）+ \左| u \ right |^{p-2} u = f（x，u）＆\ text {in}＆ω， \ hspace {3,4cm} u = 0＆\ text {in}＆m \setMinusΩ， \ end {array} \ right。 \ end {收集} \ end {eqnarray} $ω$是具有光滑边界的M的开放式子集。
In this paper, we investigate the existence and uniqueness of a non-trivial solution for a class of nonlocal equations involving the fractional $p$-Laplacian operator defined on compact Riemannian manifold, namely, \begin{eqnarray}\label{k1} \begin{gathered} \left\{\begin{array}{lll} (-Δ_g)^s_p u(x)+ \left| u \right|^{p-2} u= f(x,u) & \text { in }& Ω, \hspace{3,4cm} u=0 & \text{in }& M\setminusΩ, \end{array}\right. \end{gathered} \end{eqnarray} and $Ω$ is an open bounded subset of M with a smooth boundary.
