On the Absence of Solutions for a~Class of Singular Semilinear Differential Inequalities

G. G. Laptev

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 223-235.

Résumé

The nonexistence of solutions to certain semilinear differential inequalities in a bounded domain is established. A model problem for such inequalities is $-\Delta u\ge |u|^q/|x|^\sigma$ ($\sigma \ge 2$) in a ball $B_R$. Similar evolution inequalities and fourth-order problems with the operator $\Delta ^2$ are analyzed. The proofs are based on the method of test functions.

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