Existence of positive pseudo-almost-periodic solution for some nonlinear infinite delay integral equations arising in epidemic problems

Solutions of Volterra integral equations with infinite delay

“…Our results generalize and complement those in [1], [4], [5], [9], [11]- [14], [16], [17], [20]. We include several examples to show the applicability of our results.…”

“…For example, in [16] Equation (1.1) is considered in the study of hereditary response in continuum physics for a material with large memory, and in [20] it is employed in the study of the response of nonlinear feedback systems to periodic input signals. We refer the reader to [1] for a brief description of the meaning of (1.1) in the context of epidemics. In [4] the relation between (1.1) and the common variation of parameters formula is discussed.…”

“…The existence of almost periodic solutions for (1.1), and as a consequence of bounded continuous solutions (see [7] for general theory on almost periodic functions), has been considered in [1], [5], [14]. In [14] the authors prove that if there exists a bounded solution with suitable stability properties then that solution is in fact an almost periodic solution.…”

“…In [5] Equation (1.1) is considered in the convolution case and existence is established using Liapunov functionals and a theorem of Schaefer type. In [1] Equation (1.1) is also considered in the convolution case with f ≡ 0 and using the Hilbert projective metric the authors show that the equation has exactly one pseudo-almost-periodic positive solution.…”

Pseudo almost periodic solutions to parabolic boundary value inverse problems

“…Like almost periodic functions, pseudo almost periodic functions are applied to many mathematical areas, particularly to ordinary differential equations (e.g., see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and references therein). However, the study of the related topic on partial differential equations has only a few important developments.…”