A new set of solutions to a singular second-order differential equation arising in boundary layer theory (Q2019052)

The paper investigates existence, non-existence and multiplicity of solutions to a boundary value problem associated with a singular second order ODE arising in boundary layer theory and governing the laminar flow of Newtonian and non-Newtonian fluids. More precisely, this equation has the form \[ g^{1/N}(x)g''(x) + h(x) = 0, \qquad \xi < x < 1, \] and is considered together with the boundary condition \(g'(\xi) = C\) and \(g(1) = 0\). Under suitable assumptions on \(h(x)\), the solvability picture of this BVP is discussed on varying of the parameters \(\xi\) and \(C\). The proofs are performed using a shooting technique, exploiting in an essential way some tools from lower/upper solutions theory.