Nonexistence of solutions to systems of higher-order semilinear inequalities in cone-like domains *

Abdallah El Hamidi (1) , Gennady G Laptev

1 LaSIE - Laboratoire des Sciences de l'Ingénieur pour l'Environnement - UMR 7356

In this paper, we obtain nonexistence results for global solutions to the system of higher-order semilinear partial differential inequalities ∂ k ui ∂t k − ∆(ai(x, t)ui(x, t)) ≥ t γ i+1 |x| σ i+1 |ui+1(x, t)| p i+1 , 1 ≤ i ≤ n, un+1 = u1, in cones and cone-like domains in R N , t > 0. Our results apply to nonneg-ative solutions and to solutions which change sign. Moreover, we provide a general formula of the critical exponent corresponding to this system. Our proofs are based on the test function method, developed by Mitidieri and Pohozaev.

Domaines: Equations aux dérivées partielles [math.AP]

Abdallah El Hamidi, Gennady G Laptev. Nonexistence of solutions to systems of higher-order semilinear inequalities in cone-like domains *. Electronic Journal of Differential Equations, 2002, 2002, pp.1 - 19. ⟨hal-02507092⟩