A Retarded Gronwall-Like Inequality and Its Applications
By Olivia Lipovan. 2000
171 citations recorded by the source corpus.
We prove a Gronwall-like inequality and present some of its applications to the qualitative study of retarded differential equations. The problems of global continuation of the solutions and the existence of nonoscillatory solutions are considered. By means of examples we show the usefulness of our results.
Subfields: Applied Mathematics, Control and Systems Engineering, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/ed66c5acdfc550abf44f4282a56b9242e287418d
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In Applied Mathematics
In Control and Systems Engineering
In Geometry and Topology
Citations in the corpus
- Some new nonlinear inequalities and applications to boundary value problems (2006, background): “Theorem F (Lipovan [11]).”
- Discrete non-linear inequalities and applications to boundary value problems (2006, background): “(Lipovan [9]) Suppose u,f are continuous non-negative functions on [x0,X), w a continuous non-decreasing function on [0,∞) with w(r) > 0 for r > 0, and α : [x0,X) → [x0,X) a continuous non-decreasing function with α(x) x on [x0,X).”
- A retarded integral inequality and its applications (2003, background): “The problem of the global existence of the solutions to (6) was also considered in [2,5,10].”
- ON THE ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS TO A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS (2003, methodology): “We can apply Schauder’s fixed point theorem [8] to deduce that F has a fixed point y ∈ K .”