New fixed point theorems for mixed monotone operators and local existence–uniqueness of positive solutions for nonlinear boundary value problems☆

By Chengbo Zhai, Lingling Zhang. 2011

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Positive solutions of fractional differential equations involving the Riemann–Stieltjes integral boundary condition (2018, unknown): “In [8], Feng and Zhai used a new fixed point theorem [19] to consider the following problem: ⎧⎨ ⎩D α 0+u(t) + λf (t, u(t), u(t)) = 0, t ∈ (0, 1), u(0) = u′(0) = 0, u(1) = ∫ 1 0 q(t)u(t) dt, where 2 < α ≤ 3, 0 < β ≤ 1 are real numbers, f : [0, 1] × [0,∞) × [0,∞) → [0,∞) is a continuous function, q : ”
The unique solution of a class of sum mixed monotone operator equations and its application to fractional boundary value problems (2016, background): “Because of the crucial role played by nonlinear equations in applied science as well as mathematics, nonlinear functional analysis has been an active area of research, and nonlinear operators with connection to nonlinear (fractional) differential and integral equations have been extensively studied ”