A CLASS OF SINGULAR FIRST ORDER DIFFERENTIAL EQUATIONS WITH APPLICATIONS IN REACTION-DIFFUSION

摘要

We study positive solutions y(u) for 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 in [0,1] such that f(0) = 0 = f(1). We shall be particularly concerned with positive 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 space 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.