Positive μ-pseudo almost periodic solutions for some nonlinear infinite delay integral equations arising in epidemiology using Hilbert’s projective metric

Abstract

The purpose of this work is to give sufficient conditions which guarantee the existence and the uniqueness of positive μ-pseudo almost periodic solutions for the nonlinear infinite delay integral equation . We improve the original work of [H. S. Ding, Y. Y. Chen and G. M. N’Guérékata, Existence of positive pseudo almost periodic solutions to a class of neutral integral equations, Nonlinear Analysis. Theorey, Methods and Applications 74 (2011) 7356-7364] by dropping the hypotheses of monotonicity on the functions f and h. The main results are proved by using the Hilbert’s projective metric combined with the contraction mapping principle. Our results can deal with some cases to which many results are not applicable. An example is provided to illustrate the main results of this work.

Keywords

• μ-pseudo almost periodic functions
• nonlinear delay integral equation
• contraction mapping principle
• hilbert’s projective metric
• positive solution
• 34c27
• 45g10
• 47h10