Abstract
In this work, we investigate the existence of positive solutions of Sturm-Liouville boundary value problems for singular nonlinear second-order impulsive integro differential equation in a real Banach space. Some new existence results of positive solutions are established by applying fixed-point index theory together with comparison theorem. Some discussions and an example are given to demonstrate the applications of our main results.
Highlights
1 Introduction In this paper, we study the existence of positive solutions to second-order singular nonlinear impulsive integro-differential equation of the form:
Boundary value problems for impulsive differential equations arise from many nonlinear problems in sciences, such as physics, population dynamics, biotechnology, and economics etc
As it is well known that impulsive differential equations contain jumps and/or impulses which are main characteristic feature in computational biology
Summary
1 Introduction In this paper, we study the existence of positive solutions to second-order singular nonlinear impulsive integro-differential equation of the form: In Section , some discussions and an example for singular nonlinear integro-differential equations are presented to demonstrate the application of the main results. A nonempty closed set P ⊂ E is called a cone if it satisfies the following two conditions: ( ) x ∈ P, λ > implies λx ∈ P; ( ) x ∈ P, –x ∈ P implies x = .
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