General existence principles for Stieltjes differential equations with applications to mathematical biology

Stieltjes Bochner spaces and applications to the study of parabolic equations

“…In this section we present a possible application of the theory that we have developed in the previous section to a silkworm population model based on the example presented in [3,Section 5]. In our case, we will consider that we have a diffusion term that allows us to study the spatial distribution of the silkworm in an island (for instance, Gran Canaria).…”

“…A detailed description of the relationship between the previous functions and the life cycle of silkworms can be found in [3]. If we integrate (125) in the whole…”

“…where we have assumed that we can interchange the integral with the Stieltjes derivative, we recover the 0-space-dimensional model studied in [3]:…”

“…The study of this type of derivatives and its application to the field of ODEs appears in [1][2][3][4]. We use the notation established in previous works.…”

“…The set D g of discontinuities of g correspond with times when sudden changes occur and which are usually introduced in the form of impulses. Finally, in the remaining set of times [0, T ] \ (C g ∪ D g ) the system presents a parabolic behavior and the different slopes of the derivator g (see [3]) correspond to different influences of the corresponding times, namely, the bigger the slope of g the more important the corresponding times are for the process. In a certain sense, system (1) can be considered as a degenerate parabolic system.…”