Chapter 1 Topological Principles for Ordinary Differential Equations

摘要: Publisher Summary This chapter discusses topological principles for ordinary differential equations. The classical courses of equations (ODEs) start either with the Peano existence theorem or Picard-Lindelof and uniqueness theorem, both related to Cauchy (initial value) problems. describes applied fixed point general methods solvability boundary value It also various theorems such as Sharkovskii cycle coexistence T. Matsuoka's theorem. illustrates (multivalued) ODEs. All solutions problems under consideration (even in Banach spaces) can be understood at least sense Caratheodory. Thus, view indicated relationship given chapter, many obtained results employed solving optimal control problems, systems variable structure, implicit etc.