Nonlinear second order ordinary differential equations with nonlocal boundary conditions. (English) Zbl 1108.34303
Summary: We investigate the existence of solutions for a class of three-point boundary value problems for second order ordinary differential equations. We consider two types of nonlinearities, continuous nonlinearities and Carathéodory nonlinearities. The methods used in the first case rely on the topological transversality theorem, and in the second case we use the technique of cut-off functions. In both cases, a priori bounds on solutions play a key role in the analysis.
MSC:
34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
34B15 | Nonlinear boundary value problems for ordinary differential equations |