Positive and dead core solutions of singular BVPs for third-order differential equations Original Research Article

The paper discusses the existence of positive and dead core solutions of the singular differential equation (ϕ(u″))′=λf(t,u,u′,u″)(ϕ(u″))′=λf(t,u,u′,u″) satisfying the boundary conditions u(0)=Au(0)=A, u(T)=Au(T)=A, min{u(t):t∈[0,T]}=0min{u(t):t∈[0,T]}=0. Here λλ is a nonnegative parameter, AA is a positive constant and the Carathéodory function f(t,x,y,z)f(t,x,y,z) is singular at the value 0 of its space variable yy.