Alan V. Lair, "A necessary and sufficient condition for uniqueness of solutions of singular differential inequalities", International Journal of Mathematics and Mathematical Sciences, vol. 13, Article ID 363475, 18 pages, 1990. https://doi.org/10.1155/S0161171290000382
A necessary and sufficient condition for uniqueness of solutions of singular differential inequalities
The author proves that the abstract differential inequality in which the linear operator , symmetric and antisymmetric, is in general unbounded, and is a positive constant has a nontrivial solution near which vanishes at if and only if . The author also shows that the second order differential inequality in which has a nontrivial solution near such that if and only if either or . Some mild restrictions are placed on the operators and . These results extend earlier uniqueness theorems of Hile and Protter.
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