A class of singular first order differential equations with applications in reaction-diffusion

We study positive solutions y(u) to the first order differential equation y'=q(cy^{1/p}-f(u)) where c>0 is a parameter, p>1 and q>1 are conjugate numbers and f is a continuous function on [0,1] such that f(0)=0=f(1). We shall be particularly concerned with solutions y(u) such that y(0)=0=y(1). Our motivation lies in the fact that this problem provides a model for the existence of travelling wave solutions for analogues of the FKPP equation in one spacial dimension, where diffusion is represented by the p-Laplacian operator. We obtain a theory of admissible velocities and some other features that generalize classical and recent results, established for p=2.