Measures of noncompactness in the study of asymptotically stable and ultimately nondecreasing solutions of integral equations

摘要

We introduce a new class of measures of noncompactness related to asymptotic stability and ultimate monotonicity in the space of continuous and bounded functions on an unbounded interval. With help of those measures of noncompactness and a.xed point theorem of Darbo type we investigate the existence of asymptotically stable and ultimately nondecreasing solutions of some quadratic functional integral equations of Hammerstein-Volterra type.