Boundary and periodic value problems for systems of nonlinear second order differential equations
The author considers the boundary and periodic value problem for system of nonlinear second order differential equations \(x''(t)=f(t,x(t),x'(t))\) a.e. \(t \in[0,1]\), \(x \in BC\), where \(f:[0,1] \times \mathbb{R}^{2n} \to \mathbb{R}^ n\) is a Carathéodory function and \(BC\) denotes a boundary condition such as non-homogeneous Dirichlet, Neumann, Sturm-Liouville conditions, or the periodic condition. Existence results are obtained on assumptions which are generalizations of the conventional assumptions for such problems. The proofs rely on the Schauder fixed point theorem.
system of nonlinear second order differential equations
scientific article; zbMATH DE number 482094