Main subject categories: • Ordinary differential equations • Differential equations • Topological principles for ordinary differential equations • Heteroclinic orbits for some classes of second and fourth order differential equations • A qualitative analysis, via lower and upper solutions, of first order periodic evolutionary equations with lack of uniqueness • Bifurcation theory of limit cycles of planar systems • Functional differential equations with state-dependent delays: Theory and applications • Global solution branches and exact multiplicity of solutions for two point boundary value problems • Singularities and Laplacians in boundary value problems for nonlinear ordinary differential equationsThis is the third volume in a series devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields, in order to make the chapters of the volume accessible to a wide audience.These ideas faithfully reflect the spirit of this multi-volume and the editors hope that it will become very useful for research, learning and teaching.This volume consists of seven chapters covering a variety of problems in ordinary differential equations. Both, pure mathematical research and real word applications are reflected pretty well by the contributions to this volume.• Covers a variety of problems in ordinary differential equations• Pure mathematical and real world applications• Written for mathematicians and scientists of many related fields