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The Method of Quasilinearization and Positivity of Solutions in Abstract Cones
(University of Texas at Arlington, 1976-03)
The method of quasilinearization was first introduced by Bellman (Ref. 1) and was developed further by Kalaba (Ref. 2). More detailed information concerning the method can be found in (Ref. 3). This method has been very ...
Maximal and Minimal Solutions and Comparison Principle for Differential Equations in Abstract Cones
(University of Texas at Arlington, 1975-06)
Existence of maximal and minimal solutions for differential equations in abstract cones is established without requiring uniform continuity. Utilizing such a result an abstract comparison principle is developed. The results ...
Monotone Iterative Technique for Differential Equations in a Banach Space
(University of Texas at Arlington, 1981-02)
Let E be a real Banach space with norm [see pdf for notation]. Consider the initial value problem (1.1) [see pdf for notation], where [see pdf for notation]. Generally speaking of approximate solutions of (1.1) consist ...