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 $$ x(t)=g(t,x(t))\int_{-\infty}^{t}a(t,t-s)f(s,x(s))ds,\quad t\in\mathbb{R}. $$ 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.

Keywords

• Quadratic integral equation
• positive solution
• cone