In this paper, the method of quasilinearization is extended to differential equations in Banach spaces using abstract cones. Frequently, it is useful to apply this technique to a comparison system. Several applications are given indicating the flexibility obtained by appropriate choice of the comparison system and cone.
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Communicated by R. E. Kalaba
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Lakshmikantham, V., Mitchell, A.R. & Sety, D.D. Method of quasilinearization and positivity of solutions in abstract cones. J Optim Theory Appl 22, 353–372 (1977). https://doi.org/10.1007/BF00932860
- Quasilinearization methods
- abstract spaces
- differential equations
- inequality theory