Nonexistence of Solutions to Systems of Higher-order Semilinear Inequalities in Cone-like Domains
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In this paper, we obtain nonexistence results for global solutions to the system of higher-order semilinear partial differential inequalities ∂kui / ∂tk - ∆(ai(x,t)ui(x,t)) ≥ t γi + 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.
CitationEl Hamidi, A., & Laptev, G. G. (2002). Nonexistence of solutions to systems of higher-order semilinear inequalities in cone-like domains. Electronic Journal of Differential Equations, 2002(97), pp. 1-19.
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