Global structure of positive solutions for a fourth-order boundary value problem with singular data

Abstract

We are concerned with a problem described the deformation of a simply supported beam of the form

for $x\in (0,1)$, where $\lambda$ is a positive parameter, $c\in C([0,1],\mathbb{R})$, $c_i\in \mathbb{R}$, $a,a_j\in C([0,\infty ),[0,\infty ))$, $i=1,2,\dots ,p$, $j=1,2,\dots ,q$, $p,q\in \mathbb{N}$. The Dirac delta impulses $\delta =\delta (x)$ are applied at given points $0<x_1<x_2<\cdots <x_p<1$ and $0<y_1<y_2<\cdots <y_q<1$. We investigate the global structure of positive solutions by the global bifurcation techniques.