Our main concern in this article is to investigate the existence of solution for the boundary-value problem $$\begin{aligned}& (\phi \bigl(x'(t)\bigr)'=g_{1} \bigl(t,x(t),x'(t)\bigr),\quad \forall t\in [0,1], \\& \Upsilon _{1}\bigl(x(0),x(1),x'(0)\bigr)=0, \\& \Upsilon _{2}\bigl(x(0),x(1),x'(1)\bigr)=0, \end{aligned}$$ where $g_{1}:[0,1]\times \mathbb{R}^{2}\rightarrow \mathbb{R}$ is an $L^{1}$ -Carathéodory function, $\Upsilon _{i}:\mathbb{R}^{3}\rightarrow \mathbb{R} $ are continuous functions, $i=1,2$ , and $\phi :(-a,a)\rightarrow \mathbb{R}$ is an increasing homeomorphism such that $\phi (0)=0$ , for $0< a< \infty $ . We obtain the solvability results by imposing some new conditions on the boundary functions. The new conditions allow us to ensure the existence of at least one solution in the sector defined by well ordered functions. These ordered functions do not require one to check the definitions of lower and upper solutions. Moreover, the monotonicity assumptions on the arguments of boundary functions are not required in our case. An application is considered to ensure the applicability of our results.

中文翻译：

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一阶导数相关的ϕ -Laplacian边值问题的存在性结果

新条件使我们能够确保在功能良好的部门定义的部门中至少存在一种解决方案。这些有序函数不需要检查下限和上限解决方案的定义。而且，在我们的情况下，不需要边界函数的参数的单调性假设。为了确保我们的结果的适用性，我们考虑了一项申请。