In this paper we are concerned with the reaction-diffusion equation ut = Δu + f(u) in a ball of RN with Dirichlet boundary condition. We assume that f satisfies the concave-convex condition. A typical example is f(u) = |u|q-1u + |u|p-1u (0 < q < 1 < p < (N+2)/(N-2)). First we obtain the complete structure of positive solutions to the stationary problem; Δφ + f(φ) = 0. Next we state the relations between this structure and time-depending behaviors of nonnegative solutions (global existence or blow up) to the non-stationary problem.
|ジャーナル||Nonlinear Analysis, Theory, Methods and Applications|
|出版物ステータス||Published - 2001 8 1|
|イベント||3rd World Congres of Nonlinear Analysts - Catania, Sicily, Italy|
継続期間: 2000 7 19 → 2000 7 26
ASJC Scopus subject areas
- Applied Mathematics