Invariant imbedding and Riccati transformations

摘要: From its inception, the theory of invariant imbedding has been concerned with study various relations between inputs and outputs physical processes. Where processes could be modelled by differential or integro-differential equations, these ideas have led to heuristic development functional relationships for solutions equations. In this work, we show that a general class two point boundary value problems can obtained from mathematical arguments rather than ones. The principal result is establishment equivalence solving family determining existence transformations on set given We refer as Riccati transformations. They are shown determined initial which generalize equations previous authors. work in coordinate free setting Banach space. usefulness approach able readily extend our results nonlocal multipoint conditions. An indication made how similar applies difference