Abstract
In this paper we study a class of sum operator equation $Ax+Bx+C(x,x)=x$ on ordered Banach spaces, where A is an increasing operator, B is a decreasing operator, and C is a mixed monotone operator. The existence and uniqueness of its positive solution are obtained by using the properties of cone and fixed point theorems for mixed monotone operators. As an application, we utilize the obtained results to study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems.
Highlights
Over the past several decades, nonlinear functional analysis has been an active area of research in mechanics, elasticity, fluid dynamics, and so on
The existence and uniqueness of its positive solutions are obtained by using the properties of cones and a fixed point theorem for increasing general β-concave operators
By using the properties of cones and a fixed point theorem for mixed monotone operators, respectively, the author established the existence and uniqueness of positive solutions for the operator equation
Summary
Over the past several decades, nonlinear functional analysis has been an active area of research in mechanics, elasticity, fluid dynamics, and so on. The existence and uniqueness of its positive solutions are obtained by using the properties of cones and a fixed point theorem for increasing general β-concave operators.
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