On the Explicit Integration of Special Types of Differential Inequalities
A general method was proposed in our previous paper for explicitly finding all solutions of the differential inequality, which is based on the general solution of the corresponding differential equation or, in other words, on the variation of arbitrary constants. Criteria of extendibility and characteristics of the maximally extended (full) solution of the inequality were proven. In this paper, we applied these results to specific types of inequalities most frequently encountered in applications and literature. We also compared them to other known methods in the literature.
Keywordsdifferential inequality linear differential inequality integrable differential inequality comparison theorems general solution variation method solution continuity
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- 2.B. G. Pachpatte, Inequalities for Differential and Integral Equations (Academic, San Diego, CA, 2007), in Ser. Mathematics in Science and Engineering, Vol. 197.Google Scholar
- 6.R. L. Pouso, “Greatest solutions and differential inequalities: A journey in two directions” (2013). arXiv 1304.3576v1 [math.CA]Google Scholar
- 10.A. B. Vasilyeva and N. N. Nefedov, Comparison Theorems. The Method of Differential Inequalities of Chaplygin (Mosk. Gos. Univ., Moscow, 2007) [in Russian].Google Scholar
- 12.Yu. N. Bibikov, General Course of Ordinary Differential Equations (S.-Peterb. Gos. Univ., S.-Peterburg, 2005) [in Russian].Google Scholar