Existence of solutions for some nonlinear problems with boundary value conditions (Q1669239)

Summary: We study the existence of solutions for nonlinear boundary value problems \(\left(\varphi \left(u'\right)\right)' = f \left(t, u, u'\right), l \left(u, u'\right) = 0\), where \(l(u, u') = 0\) denotes the boundary conditions on a compact interval \(\left[0, T\right]\), \(\varphi\) is a homeomorphism such that \(\varphi(0) = 0\), and \(f : \left[0, T\right] \times \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}\) is a continuous function. All the contemplated boundary value problems are reduced to finding a fixed point for one operator defined on a space of functions, and Schauder fixed point theorem or Leray-Schauder degree is used.