Geodesic
On Differential Inequalities with Point Singularities on the Boundary
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 119-129

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We prove the nonexistence of solutions for some nonlinear ordinary differential equations and inequalities, for quasilinear partial differential equations and inequalities in bounded domains with singular points on the boundary, and for systems of such equations and inequalities. The proofs are based on the method of nonlinear capacity. We also give examples demonstrating that the conditions obtained are sharp in the class of problems under consideration. 
@article{TM_2008_260_a7,
     author = {E. I. Galakhov},
     title = {On {Differential} {Inequalities} with {Point} {Singularities} on the {Boundary}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {119--129},
     publisher = {mathdoc},
     volume = {260},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_260_a7/}
}
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E. I. Galakhov. On Differential Inequalities with Point Singularities on the Boundary. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and nonlinear partial differential equations, Tome 260 (2008), pp. 119-129. http://geodesic.mathdoc.fr/item/TM_2008_260_a7/