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Existence of solutions for anti-periodic boundary value problems of nonlinear impulsive functional integro-differential equations of mixed type. (English) Zbl 1179.45008
The authors discuss the existence of minimal and maximal solutions for a class of first order nonlinear impulsive functional integro-differential equations of mixed type with anti-periodic boundary conditions. Keeping in view the importance of functional integro-differential equations and anti-periodic boundary conditions, they apply the monotone iterative technique (MIT) to prove the existence of extremal solutions for a first order nonlinear impulsive functional integro-differential equation of mixed type with anti-periodic boundary conditions. The MIT coupled with the method of upper and lower solutions manifests itself as an effective and flexible mechanism that offers theoretical as well as constructive existence results in a closed set, generated by the lower and upper solutions.
45J05Integro-ordinary differential equations
45L05Theoretical approximation of solutions of integral equations
45G10Nonsingular nonlinear integral equations