Abstract
In this paper, we consider a class of integral boundary value problems for nonlinear third-order impulsive integro-differential equation with a monotone homomorphism in real Banach space. By employing fixed point index theory, some sufficient criteria are obtained to ensure the existence of positive solutions. An example is given to demonstrate the application of our main results.
Highlights
1 Introduction This paper deals with the existence of positive solutions for the following nonlinear thirdorder impulsive integro-differential equation with monotone homomorphism and integral boundary value conditions in real Banach space (abbreviated by BVP ( . ) throughout this paper):
P is a positive cone in E. θ is a zero element of E. f ∈ C[J × P, P], Ik ∈ C[P, P], Ik ∈ C[P, P]. g ∈ L [, ] is nonnegative. φ : P → E is an increasing and positive homomorphism and φ(θ ) = θ . x|t=tk = x(tk+) – x(tk–), x |t=tk = x – x. x(tk+), x and x(tk–), x represent the right-hand limits and left-hand limits of x(t) and x (t) at t = tk, respectively. (Tx)(t) and (Sx)(t) are defined as t
In [ ], Fu and Ding considered the existence of positive solutions of the boundary value problems with integral boundary conditions in Banach spaces of the form (φ(–x (t))) = f (t, x(t)), t ∈ J, x( ) = x ( ) = θ, x( ) =
Summary
1 Introduction This paper deals with the existence of positive solutions for the following nonlinear thirdorder impulsive integro-differential equation with monotone homomorphism and integral boundary value conditions in real Banach space The fixed point principle in cone is one of the important methods by applying to investigate the existence and multiplicity of positive solutions for boundary value problems. In [ ], Fu and Ding considered the existence of positive solutions of the boundary value problems with integral boundary conditions in Banach spaces of the form (φ(–x (t))) = f (t, x(t)), t ∈ J, x( ) = x ( ) = θ, x( ) =
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