The theory of forced, convex, autonomous, two point boundary value problems (Q1088038)

The author considers the boundary value problem \[ u''+bu'+\lambda f(u)=0,\quad \alpha_ 0u(0)-\alpha_ 0'u'(0)=\gamma_ 0,\quad \alpha_ 1u(1)+\alpha_ 1u'(1)=\gamma_ 1 \] where the function \(f: {\mathbb{R}}_+\to {\mathbb{R}}_+\) \(({\mathbb{R}}_+=[0,+\infty [)\) is convex, \(b\in {\mathbb{R}}\), \(\gamma_ 1,\gamma_ 2\in {\mathbb{R}}_+\), the nonnegative constants \(\alpha_ i,\alpha_ i'\) \((i=0,1)\) satisfy certain restrictions and \(\lambda\) is a positive parameter. He studies the dependence of the structure of nonnegative solutions on \(\lambda\).