Sign-changing stationary solutions and blowup for the two power nonlinear heat equation in a ball

Consider the nonlinear heat equation(0.1)ut=Δu+|u|p−1u−|u|q−1u, where t≥0 and x∈Ω, the unit ball of RN, N≥3, with Dirichlet boundary conditions. Let h be a radially symmetric, sign-changing stationary solution of (0.1). We prove that the solution of (0.1) with initial value λh blows up in finite time if |λ−1|>0 is sufficiently small and if 1