This article is cited in 1 paper

Mathematics

On solution of a class of Hammerstein type nonlinear integral equations on the positive half-line in the critical case

H. S. Petrosyan

National Agrarian University of Armenia

Abstract: In the this article a class of nonlinear integral equations with noncompact Hammerstein integral operator, the kernel of which depends on difference of its arguments is investigated. Above mentioned class of equations arises in the kinetic theory of gases and in the radiative transfer theory in nuclear reaction.
Combination of special iteration methods with the methods of the theory of construction of invariant cone-shaped segments allow to prove existence theorems of positive solutions in special selected weighted space.

Keywords: Hammerstein type equation, completely monotone kernel, iteration, Caratheodory’s condition, monotony, convergence.

MSC: Primary 45G05; Secondary 47H30

Received: 05.05.2014
Accepted: 23.06.2014

Language: English