A class of singular n -dimensional impulsive Neumann systems

This paper investigates the existence of infinitely many positive solutions for the second-order n-dimensional impulsive singular Neumann system $$\begin{aligned}& -\mathbf{x}^{\prime\prime}(t)+ M\mathbf{x}(t)=\lambda {\mathbf{g}}(t)\mathbf{f} \bigl(t,\mathbf{x}(t) \bigr),\quad t\in J, t\neq t_{k}, \\& -\Delta {\mathbf{x}}^{\prime}|_{t=t_{k}}=\mu {\mathbf{I}}_{k} \bigl(t_{k},\mathbf{x}(t_{k}) \bigr),\quad k=1,2,\ldots ,m, \\& \mathbf{x}^{\prime}(0)=\mathbf{x}^{\prime}(1)=0. \end{aligned}$$ The vector-valued function x is defined by $$\begin{aligned}& \mathbf{x}=[x_{1},x_{2},\dots ,x_{n}]^{\top }, \qquad \mathbf{g}(t)=\operatorname{diag} \bigl[g_{1}(t), \ldots ,g_{i}(t), \ldots , g_{n}(t) \bigr], \end{aligned}$$ where \(g_{i}\in L^{p}[0,1]\) for some \(p\geq 1\), \(i=1,2,\ldots , n\), and it has infinitely many singularities in \([0,\frac{1}{2})\). Our methods employ the fixed point index theory and the inequality technique.