Abstract
Using the technique of a suitable measure of non-compactness and the Darbo fixed point theorem, we investigate the existence of a nonlinear functional integral equation of Urysohn type in the space of Lebesgue integrable functions Lp(RN). In this space, we show that our functional-integral equation has at least one solution. Finally, an example is also discussed to indicate the natural realizations of our abstract result.
Highlights
Integral equations appear in many applications in describing numerous real world problems (see, for instance, ([30], [31], [5], [18]), and references therein)
Many useful applications in describing problems of the real world and numerous events, which appear in physics, engineering, mechanics, biology, etc
Apart from that, integral equations are often investigated in research papers and monographs and the references cited therein
Summary
Integral equations appear in many applications in describing numerous real world problems (see, for instance, ([30], [31], [5], [18]), and references therein). See for example [1, 4, 8, 13, 15] can be depicted and demonstrated by methods of non-linear functional integral equations (for example, we refer to [25, 26, 28]). Apart from that, integral equations are often investigated in research papers and monographs (cf [6, 12, 16, 18, 29, 32]) and the references cited therein
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