### A model of frontal polymerization using complex initiation.

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We prove an existence theorem for connected branches of solutions to nonlinear operator equations in Banach spaces. This abstract result is applied to the asymptotically equivalent solutions to nonlinear ordinary differential equations.

This paper is concerned with the asymptotic expansion and numerical solution of systems of linear delay differential equations with highly oscillatory forcing terms. The computation of such problems using standard numerical methods is exceedingly slow and inefficient, indeed standard software is practically useless for this purpose. We propose an alternative, consisting of an asymptotic expansion of the solution, where each term can be derived either by recursion or by solving a non-oscillatory...

Tumour immunotherapy is aimed at the stimulation of the otherwise inactive immune system to remove, or at least to restrict, the growth of the original tumour and its metastases. The tumour-immune system interactions involve the stimulation of the immune response by tumour antigens, but also the tumour induced death of lymphocytes. A system of two non-linear ordinary differential equations was used to describe the dynamic process of interaction between the immune system and the tumour. Three different...

The paper describes asymptotic properties of a strongly nonlinear system $\dot{x}=f(t,x)$, $(t,x)\in \mathbb{R}\times {\mathbb{R}}^{n}$. The existence of an $\lfloor n/2\rfloor $ parametric family of solutions tending to zero is proved. Conditions posed on the system try to be independent of its linear approximation.

In the paper it is shown that each solution $u(r,\alpha )$ ot the initial value problem (2), (3) has a finite limit for $r\to \infty $, and an asymptotic formula for the nontrivial solution $u(r,\alpha )$ tending to 0 is given. Further, the existence of such a solutions is established by examining the number of zeros of two different solutions $u(r,\overline{\alpha})$, $u(r,\widehat{\alpha})$.