Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 97, pp. 1-19.

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

Authors: Abdallah El Hamidi (Univ. de La Rochelle, France)
         Gennady G. Laptev (Steklov Mathematical Institute, Russia)
         
Abstract: 
  In this paper, we obtain nonexistence results for global
  solutions to the system of higher-order semilinear partial
  differential inequalities
  $$\displaylines{
  \frac{\partial^k u_i}{\partial t^k}-\Delta (a_i (x,t) u_i (x,t))
  \geq t^{\gamma_{i+1}}|x|^{\sigma_{i+1}} |u_{i+1} (x,t) |^{p_{i+1}},
  \quad 1 \leq i \leq n, \cr
  u_{n+1}=u_1,
  }$$
  in cones and cone-like domains in $\mathbb{R}^N$, $t>0$.
  Our results apply to nonnegative 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.
   
Submitted March 10, 2002. Published November 14, 2002.
Math Subject Classifications: 35G25, 35R45.
Key Words: nonexistence; blow-up; higher-order differential
           inequalities; critical exponent.