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中文摘要：
利用上下解和单调迭代法，研究了带Neumann边界条件的二阶泛函微分φ-Laplace方程在上下解反序条件下解的存在性条件．解在区间[β，α]上的存在性由反极大值原理给出，这样的比较原理是基本的，确保了可以利用单调迭代法来证明极值解的存在性．
英文摘要：
This paper deals with the existence conditions to second order functional differential φ-Laplace equation with Neumann boundary value conditions by the method of upper and lower solutions and monotone iterative technique. Moreover,it obtains the existence conditions with upper and lower solutions in the reverse order. The existence of solutions in [β,α] is given via anti-maximum principles. Such comparison principles are fundamental and ensure both the existence and the approximation of extremal solutions of problems via the monotone method.
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