Street, Brian2022-07-272022-07-272017-09-21Street, B. (2017). Differential equations with a difference quotient. <i>Electronic Journal of Differential Equations, 2017</i>(227), pp. 1-42.1072-6691https://hdl.handle.net/10877/15996The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of such a differential equation, is for a polynomial P and continuous functions ƒ(t, x) : [0, 1] x [0, 1] → ℝ, ∂/∂t ƒ(t, x) = P(ƒ(t, x)) - P(ƒ(t, 0))/x, x > 0. These differential equations are related to inverse problems.Text42 pages1 file (.pdf)enAttribution 4.0 InternationalIll-posedDifferential equation with difference quotientExistence without uniquenessUniqueness without existenceInverse problemArticle