Multiplicity results for a three-point boundary value problem at resonance.
This paper deals with the three-point boundary value problem \[ u''=f(t,u) \quad \text{for}\;t\in(0,1), \quad u(0)=0,\;u(1)=\alpha u(\eta), \] where \(f:[0,1]\times \mathbb R\times \mathbb R\) is continuous, \(\alpha\in(0,\infty)\) and \(\eta\in(0,1)\) are given constants such that \(\alpha\eta=1\). We develop the method of lower and upper solutions by connectivity properties of the solution set of parameterized families of compact vector fields. As applications of these method, we get several multiplicity results for the problems under consideration.
scientific article; zbMATH DE number 1910237