Nonexistence of Solutions to Systems of Higher-order Semilinear Inequalities in Cone-like Domains
Date
2002-11-14
Authors
El Hamidi, Abdallah
Laptev, Gennady G.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
In this paper, we obtain nonexistence results for global solutions to the system of higher-order semilinear partial differential inequalities
∂kui/ ∂tk - ∆(αi(x, t)ui(x, t)) ≥ tγi+1|x|σi+1|ui+1 (x, t)|Pi + 1, 1 ≤ i ≤ n,
un+1 = u1,
in cones and cone-like domains in ℝN, 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.
Description
Keywords
Nonexistence, Blow-up, Higher-order differential inequalities, Critical exponent
Citation
El Hamidi, A., & Laptev, G. G. (2002). Nonexistence of solutions to systems of higher-order semilinear inequalities in cone-like domains. <i>Electronic Journal of Differential Equations, 2002</i>(97), pp. 1-19.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.