Generalized Abel Equation

Abstract

AbstractGeneralized Abel equations have the form $$ \phi \left( {F\left( x \right)} \right) = g\left( {x,\phi \left( x \right)} \right) $$ ((3.0.1)) where F : M → M is a given mapping, g(x, y) is a given function of x ∈ M, y∈ℝ and φ(x) is a solution. The Abel, Schröder and cohomological equations are particular cases of (3.0.1). Our aim is to find solvability conditions and, if possible, to describe the set of solutions of equation (3.0.1) in terms of F(x) and g(x, y).KeywordsLocal SolutionHomogeneous EquationUnique Fixed PointLocal SolvabilityGlobal SolvabilityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.