Abstract
This paper investigates the nonlinear boundary value problem for a class of first-order impulsive functional differential equations. By establishing a comparison result and utilizing the method of upper and lower solutions, some criteria on the existence of extremal solutions as well as the unique solution are obtained. Examples are discussed to illustrate the validity of the obtained results.
Highlights
It is realized that the theory of impulsive differential equations provides a general framework for mathematical modelling of many real world phenomena
It is known that the method of upper and lower solutions coupled with the monotone iterative technique is a powerful tool for obtaining existence results of nonlinear differential equations 2
There are numerous papers devoted to the applications of this method to nonlinear differential equations in the literature, see 3–9 and references therein
Summary
It is realized that the theory of impulsive differential equations provides a general framework for mathematical modelling of many real world phenomena. It is known that the method of upper and lower solutions coupled with the monotone iterative technique is a powerful tool for obtaining existence results of nonlinear differential equations 2. Only a few papers have implemented the technique in nonlinear boundary value problem of impulsive differential equations 5, 12. Journal of Inequalities and Applications nonlinear boundary value problem of a class of first-order impulsive functional differential equations. Such equations include the retarded impulsive differential equations as special cases 5, 12–14.
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