Existence of positive solutions for a nonlinear quadratic integral equation

Abstract

In this article, we study the existence of positive solutions for the nonlinear quadratic integral equation x(t) = g(t, x(t)) ∫t-∞ α(t, t - s) ƒ(s, x(s))ds, t ∈ ℝ. By using fixed point theory on cones, we prove the existence and uniqueness of bounded and continuous solution with positive infimum. An example illustrates the abstract result.