Geodesic
Nonexistence of solutions to systems of higher-order semilinear inequalities in cone-like domains
Electronic Journal of Differential Equations, Tome 2002 (2002).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\mathbb{R}^N, t greater than 0$. 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.
Classification : 35G25, 35R45
Keywords: nonexistence, blow-up, higher-order differential inequalities, critical exponent 
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     author = {El Hamidi, Abdallah and Laptev, Gennady G.},
     title = {Nonexistence of solutions to systems of higher-order semilinear inequalities in cone-like domains},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a229/}
}
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El Hamidi, Abdallah; Laptev, Gennady G. Nonexistence of solutions to systems of higher-order semilinear inequalities in cone-like domains. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a229/