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Equations containing locally Henstock-Kurzweil integrable functions

Seppo Heikkilä, Guoju Ye (2012)

Applications of Mathematics

A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions.

Equations with discontinuous nonlinear semimonotone operators

Nguyen Buong (1999)

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to present an existence theorem for the operator equation of Hammerstein type x + K F ( x ) = 0 with the discontinuous semimonotone operator F . Then the result is used to prove the existence of solution of the equations of Urysohn type. Some examples in the theory of nonlinear equations in L p ( Ω ) are given for illustration.

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