We obtain a new fixed point index theory for a class of not necessarily continuous operators in cones. We employ this tool to prove a discontinuous version of Leggett–Williams’ fixed point theorem. Finally, we establish new existence and multiplicity criteria for a second-order three point BVP with discontinuous nonlinearities.

中文翻译：

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不连续算子的不动点索引和锥中的不动点定理及其应用

我们为锥中的一类不一定连续的算子获得了新的不动点索引理论。我们使用该工具来证明Leggett–Williams不动点定理的不连续形式。最后，我们为具有不连续非线性的二阶三点BVP建立了新的存在性和多重性准则。