Parameter Dependence of Positive Solutions for Second-Order Singular Neumann Boundary Value Problems with Impulsive Effects

Abstract

The author considers the Neumann boundary value problem $-y^{\prime \prime }\left(t\right)+\mathbf{M}y\left(t\right)=\lambda \omega \left(t\right)f\left(t,y\left(t\right)\right),\mathrm{ }\mathrm{ }$ $t\in J,\mathrm{ }\mathrm{ }t\ne t_k,-\mathrm{\Delta }{y}^{\prime }{|}_{t=t_k}$ = $\lambda I_k\left(t_k,y\left(t_k\right)\right),\mathrm{ }k=\mathrm{1,2},\dots ,m,y^{\prime }(0)=y^{\prime }(1)=0$ and establishes the dependence results of the solution on the parameter $\lambda$, which cover equations without impulsive effects and are compared with some recent results by Nieto and O’Regan.