• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제17권2호
• /
• pp.175-183
• /
• 2010

Using Darbo's fixed point theorem, we establish the existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.

• Nonlinear Functional Analysis and Applications
• /
• 제28권1호
• /
• pp.57-79
• /
• 2023

We investigate the existence and uniform attractivity of solutions of a class of functional integral equations which contain a number of classical nonlinear integral equations as special cases. Using the technique of measures of noncompactness and a fixed point theorem of Darbo type we prove the existence of solutions of these equations in the Banach space of continuous and bounded functions on the nonnegative real half axis. Our results extend and improve some known results in the recent literature. An example illustrating the main result is presented in the last section.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제15권4호
• /
• pp.253-265
• /
• 2011

In this paper, we study the existence of mild solutions for double perturbed impulsive neutral functional evolution equations with infinite delay in Banach spaces. The existence of mild solutions to such equations is obtained by using the theory of the Hausdorff measure of noncompactness and Darbo fixed point theorem, without the compactness assumption on associated evolution system. An example is provided to illustrate the theory.