After different variables and functions changes, the generalized dispersal problem, recalled in (1) below and considered in part I, see Labbas et al. (Boll Unione Math Ital, to appear, 2023), leads us to consider, to study and to invert the sum of linear operators (4) below in a suitable Banach space by using two strategies: namely the theory of sums of operators in Banach spaces as developed by Da Prato–Grisvard (J Math Pures Appl 54:305–387, 1975) and successfully improved by Dore–Venni (Math Z 196:189–201, 1987).
