Positive solution for three-point boundary value problems with sign changing nonlinearities.
The authors obtain an existence result on one positive solution of the second-order three-point boundary value problem \[ u''(t)=h(t)f(t,\,u(t)),\qquad 0\leq t\leq 1,\quad u(0)-\beta u'(0)=0,\qquad u(1)=\alpha u(\eta), \] where \(f:[0,\,1]\times[0,\,\infty)\to \mathbb{R}\) is continuous, \(h:[0,\,1]\to [0,\,\infty)\) is Lebesgue integrable and \(\int_0^1h(t)\,dt>0\), \(\eta\in (0,\,1)\), \(0<\alpha<1\) and \(\beta>0\). The main trait of this paper is that it allows \(f\) to change sign. The argument is based on the topological degree theory in cones.
scientific article; zbMATH DE number 2138606