In this paper, we investigate the existence of monotone positive solutions for a fourth order boundary value problem with dependence on the derivative in nonlinearity under integral and multi-point boundary conditions. By applying the fixed point theorem in a cone, some criteria on the existence of positive solutions are acquired. These criteria are given by explicit conditions which are generally weaker than those derived by using the classical norm-type expansion and compression theorem. As applications, three examples are presented to illustrate the validity of our mains results.

中文翻译：

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混合积分和多点边界条件的四阶边值问题的单调正解

在本文中，我们研究了依赖于积分和多点边界条件下非线性导数的四阶边值问题的单调正解的存在性。通过将不动点定理应用在圆锥中，获得了一些关于正解存在性的标准。这些条件由显式条件给出，这些条件通常比使用经典范型展开和压缩定理得出的条件要弱。作为应用，提出了三个例子来说明我们的电源结果的有效性。