The existence of upper and lower solutions to second order random impulsive differential equation with boundary value problem
Zihan Li, Xiao‐Bao Shu, Fei Xu
Abstract
In this article, we consider the existence of upper and lower solutions to a second-order random impulsive differential equation. We first study the solution form of the corresponding linear impulsive system of the second-order random impulsive differential equation. Based on the form of the solution, we define the resolvent operator. Then, we prove that the fixed point of this operator is the solution to the equation. Finally, we construct the sum of two monotonic iterative sequences and prove that they are convergent. Thus, we conclude that the system has upper and lower solutions.
Topics & Concepts
MathematicsMonotonic functionResolventUpper and lower boundsOperator (biology)Boundary value problemMathematical analysisOrder (exchange)Initial value problemDifferential equationApplied mathematicsRepressorBiochemistryFinanceTranscription factorEconomicsChemistryGeneNonlinear Differential Equations AnalysisDifferential Equations and Numerical MethodsStability and Controllability of Differential Equations