Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 52, No. 3, pp. 289-299 (1995)

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Nonexistence of Global Solutions to Some Differential Inequalities of the Second Order and Applications

Philippe Souplet

Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie,
4, place Jussieu, 75252 Paris Cedex 05 - FRANCE

Abstract: We establish the nonexistence of global nondecreasing positive solutions for a class of differential inequalities of the type $u''+u'^p \geq u^q$. As a consequence, we prove the non global character of the solutions for nonlinear wave equations of the type $u_{tt}-\Delta u+u_t=\lambda u+|u|^q$, when the initial data have positive projections on the first eigenvector and a similar result for a heat equation with memory.

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