A new approach to boundary value problems on the half line using weakly-strongly sequentially continuous maps (Q2479303)

The authors use a new Leray-Schauder alternative for weakly-strongly sequentially continuous maps [see \textit{R. P. Agarwal, D. O'Regan} and \textit{X. Z. Liu}, Fixed Point Theory Appl. 2005, No.~1, 1--10 (2005; Zbl 1098.47046)] to present a new approach to establish existence principles for boundary value problems on the half line. Then they apply the new theory to obtain the existence of at least one solution to the boundary value problem \[ \begin{gathered} y''-m^2y+ f(t,y)=0 \text{ a.e. on }[0,\infty),\\ y(0)=0,\quad \lim_{t\to +\infty}y(t)=0 \end{gathered} \] where \(m>0\) is a constant and \(f: [0,\infty)\times {\mathbb R} \to {\mathbb R}\) is an \(L^p\)-Carathéodory function, with \(p>1.\)