Solvability of an infinite system of integral equations on the real half-axis

Abstract

The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

Keywords

• space of functions continuous and bounded on the half-axis
• sequence space
• measure of noncompactness
• fixed point theorem of darbo type
• infinite system of integral equations
• primary 47h08
• secondary 45g1