Geodesic
On the Absence of Solutions for a~Class of Singular Semilinear Differential Inequalities
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 223-235

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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. 
@article{TM_2001_232_a18,
     author = {G. G. Laptev},
     title = {On the {Absence} of {Solutions} for {a~Class} of {Singular} {Semilinear} {Differential} {Inequalities}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {223--235},
     publisher = {mathdoc},
     volume = {232},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2001_232_a18/}
}
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G. G. Laptev. On the Absence of Solutions for a~Class of Singular Semilinear Differential Inequalities. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, harmonic analysis, and differential equations, Tome 232 (2001), pp. 223-235. http://geodesic.mathdoc.fr/item/TM_2001_232_a18/