Abstract
This paper is concerned with a class of boundary value problems for the nonlinear impulsive functional integro-differential equations with a parameter by establishing new comparison principles and using the method of upper and lower solutions together with monotone iterative technique. Sufficient conditions are established for the existence of extremal system of solutions for the given problem. Finally, we give an example that illustrates our results.
Highlights
Impulsive differential equations have become more important in recent years in some mathematical models of real processes and phenomena studied in physics, chemical technology, biotechnology and economics
EJQTDE, 2013 No 4, p. 1 mathematical modelling of many physical phenomena. It is more accurate than the average differential equations to describe the objective world
The existence of solutions for the BVPS of these equations have been studied by many authors([11]-[13])
Summary
Impulsive differential equations have become more important in recent years in some mathematical models of real processes and phenomena studied in physics, chemical technology, biotechnology and economics. 1 mathematical modelling of many physical phenomena It is more accurate than the average differential equations to describe the objective world. We are concerned with the following BVPS for the nonlinear mixed impulsive functional integro-differential equations with a parameter: u′(t) = f (t, u(t), u(α(t)), T u, Su, ̺). (ii) If aj = 1 + λ1, ηi = 0, λ2 = k = 0, ai = 0, (i = 1, 2, j − 1, j + 1, · · · p) the Eq(1.1) reduces to the anti-periodic boundary value problem which has been studied in ([3] [17] [19]).
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