In this paper, we develop a fixed point index theory for decomposable multivalued maps, that is, compositions of two multivalued nonlinear upper semicontinuous maps. As an application, this fixed point index theory is combined with the method of lower and upper solutions in order to obtain new existence, localization and multiplicity results for $\varphi$-Laplacian problems with discontinuous nonlinearities and nonlinear functional boundary conditions.

中文翻译：

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可分解多值图的不动点索引理论及其在不连续点上的应用 $\varphi$-拉普拉斯问题

在本文中，我们开发了可分解的多值映射的不动点索引理论，即由两个多值非线性上半连续映射组成。作为应用，此定点索引理论与上下解方法相结合，以获得新的存在性，局部性和多重性结果。$\varphi$具有不连续非线性和非线性功能边界条件的拉普拉斯问题。