Applications of topological transversality to differential equations. I. Some nonlinear diffusion problems

Andrzej Granas, Ronald Bernard Guenther and John Walter Lee

Vol. 89 (1980), No. 1, 53–67

DOI: 10.2140/pjm.1980.89.53

Abstract

In this paper, topological techniques are used to establish existence results for some boundary value problems arising in diffusion theory. Questions of uniqueness are also treated. Our topological arguments are based on the topological transversality theorem rather than the Leray-Schauder theory. An important feature of our approach is that some of the results obtained cannot be deduced by a direct application of the latter theory. Further applications of topological transversality to differential equations will be given in forthcoming parts of the paper.

Mathematical Subject Classification 2000

Primary: 60J60

Secondary: 35G15, 57R99

Milestones

Received: 6 September 1979

Published: 1 July 1980