Multiplicity of sign-changing solutions for some four-point boundary value problem (Q939404)

The authors use Leray-Schauder degree theory and the upper and lower solution method to obtain at least four sign-changing solutions, at least two positive solutions and two negative solutions for the second order four-point boundary value problem: \[ y''(t)+f(t,y(t),y'(t))=0,\quad 0<t<1, \] \[ y(0)=\alpha_1 y(\eta_1),\quad y(1)=\alpha_2 y(\eta_2), \] where \(0\leq\alpha_1, \alpha_2\leq 1\), \(0<\eta_1<\eta_2<1\), \(f\in C([0,1]\times \mathbb{R}^2, \mathbb{R})\).