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Moore, R.E. (1984) Upper and Lower Bounds on Solutions of Differential, Integral Equations without Using Monotonicity, Convexity or Maximum Principle., In: Vichnevetsky, R. and Stepheman, R., Eds., Advances in Computer Methods for Partial Differential Equations, IMACS, 458-461.

has been cited by the following article:

• TITLE: Interval Analytic Method in Existence Result for Hyperbolic Partial Differential Equation

  AUTHORS: Peter O. Arawomo

  KEYWORDS: Interval Functions, Interval Majorant, Interval Extension, Interval Operator, Nested Sequence

  JOURNAL NAME: Advances in Pure Mathematics, Vol.4 No.4, April 23, 2014

  ABSTRACT: Without the usual assumption of monotonicity, we establish some results on the theory of hyperbolic differential inequalities which enable us to produce a majorising interval function for the solution of the hyperbolic initial value problem. Using this function, a variation of parameters formula and interval iterative technique, the existence of solution to the problem is established.