Abstract
The cone theory and monotone iterative technique are used to investigate the minimal nonnegative solution of nonlocal boundary value problems for second-order nonlinear impulsive differential equations on an infinite interval with an infinite number of impulsive times. All the existing results obtained in previous papers on nonlocal boundary value problems are under the case of the boundary conditions with no impulsive effects or the boundary conditions with impulsive effects on a finite interval with a finite number of impulsive times, so our work is new. Meanwhile, an example is worked out to demonstrate the main results.
Highlights
The theory of impulsive differential equations describes processes which experience a sudden change of their state at certain moments
We only consider the differential equation, integrodifferential equation, functional differential equations, or dynamic equations on time scales on a finite interval with a finite number of impulsive times
In 5, by using fixed-point index theory for cone mappings, Guo and Liu investigated the existence of multiple positive solutions of a boundary value problem for the following second-order impulsive differential equation:
Summary
The theory of impulsive differential equations describes processes which experience a sudden change of their state at certain moments. In 5 , by using fixed-point index theory for cone mappings, Guo and Liu investigated the existence of multiple positive solutions of a boundary value problem for the following second-order impulsive differential equation:. In 6 , by using fixed-point theory, Guo established the existence of solutions of a boundary value problem for the following second-order impulsive differential equation in a Banach space E :. In 31 , Guo investigated the minimal nonnegative solution of the following initial value problem for a second order nonlinear impulsive integrodifferential equation of Volterra type on an infinite interval with an infinite number of impulsive times in a Banach space E:. In this paper, we will use the cone theory and monotone iterative technique to investigate the existence of minimal nonnegative solution for a class of second-order nonlinear impulsive differential equations on an infinite interval with an infinite number of impulsive times.
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