Singular integral equations with applications to travelling waves for doubly nonlinear diffusion

The goal of this article is to offer a series of results related to the existence and properties of wavefront solutions for doubly nonlinear diffusion-reaction equations involving the p-Laplacian operator in terms of the constitutive functions of the problem. These results are derived from the analysis of singular Volterra integral equations that appear in the study of monotone travelling-wave solutions for such equations. Our results extend the ones due to B. Gilding and R. Kersner for the case p = 2 to p > 1. The fact that p not equal 2 modifies the nature of the singularity in the integral equation, and introduces the need to develop some new tools and ideas for the analysis.