On the stability properties of nonnegative solutions of semilinear problems with convex or concave nonlinearity

[摘要] We investigate the stability of nontrivial nonnegative stationary solutions of semilinear initial-boundary value problems with convex or concave nonlinearity. In the convex case f(0) less than or equal to 0 implies instability, in the concave case f(0) greater than or equal to 0 implies stability. We also discuss the necessity of the sign condition on f(0). (C) 2001 Published by Elsevier Science B.V.

[发布日期] 2001-06-01

[关键词] semilinear equations;stability of stationary solutions;convex or concave nonlinearity