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In this paper, by studying the solutions of the abstract operator equation A(x,x)+B(x,x)+e=x $A(x,x)+B(x,x)+e=x$ on ordered Banach spaces, where A, B are two mixed monotone operators and e∈P with θ≤e≤h $\theta \leq e\leq h$, we prove a class of boundary value problems on elastic beam equation to have a unique solution. Furthermore, we also apply our abstract result to establish the existence...
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