Parameter dependence of positive solutions for second-order singular Neumann boundary value problems with impulsive effects. (English) Zbl 1474.34066

Zhang, Xuemei

Abstr. Appl. Anal. 2014, Article ID 968792, 6 p. (2014).

Summary: The author considers the Neumann boundary value problem \(-y''(t)+\mathbf My(t)=\lambda\omega(t)f(t,y(t))\), \(t\in J\), \(t\neq t_k\), \(-\Delta y'|_{t=t_k}=\lambda I_k(t_k,y(t_k))\), \(k=1,2,\dots,m\), \(y'(0)=y'(1)=0\) 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.

MSC:

34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34B18	Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B37	Boundary value problems with impulses for ordinary differential equations

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