Regions of existence for a class of nonlinear diffusion type problems

Abstract

The regions of existence are established for a class of two point nonlinear diffusion type boundary value problems (NDBVP) ?S??(x)- ns?(x)- m x s?(x) = f(x,s), m > 0, n ? R, x ? (0,1), s?(0) = 0, a1s(1) + a2s?(1) = C, where a1 > 0, a2 ? 0, C ? R. These problems arise very frequently in many branches of engineering, applied mathematics, astronomy, biological system and modern science (see the existing literature of this paper). By using the concept of upper and lower solutions with monotone constructive technique, we derive some sufficient conditions for existence in the regions where ?f/?s ? 0 and ?f/?s ? 0. Theoretical methods are applied for a set of problems which arise in real life.