Existence of three solutions for a nonautonomous two point boundary value problem
Here, the author considers the two-point boundary value problem \[ u''+\lambda f(t,u)= 0,\quad u(a)= u(b)= 0,\tag{1} \] where \(f:[a, b]\times \mathbb{R}\to \mathbb{R}\) is a continuous function. Under some assumptions with respect to \(f(t,u)\) there exist an open interval \(\Lambda\subseteq ]0,+\infty[\) and a positive real number \(q\) such that, for each \(\lambda\in\Lambda\), the problem (1) admits at least three solutions belonging to \(C^2([a, b])\), whose norms in \(W^{1,2}_0([a, b])\) are less than \(q\).
scientific article; zbMATH DE number 1563078