Existence of positive solutions for a nonlinear quadratic integral equation

Wang, Chu-Hang; Ding, Hui-Sheng; N'Guerekata, Gaston

Existence of positive solutions for a nonlinear quadratic integral equation

Files

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Date

2019-06-10

Authors

Wang, Chu-Hang

Ding, Hui-Sheng

N'Guerekata, Gaston

Publisher

Texas State University, Department of Mathematics

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.

Keywords

Quadratic integral equation, Positive solution, Cone

Citation

Wang, C. H., Ding, H. S., & N'Guerekata, G. M. (2019). Existence of positive solutions for a nonlinear quadratic integral equation. <i>Electronic Journal of Differential Equations, 2019</i>(79), pp. 1-11.