Abstract In this paper, we consider a class of critical concave convex Ambrosetti–Prodi type problems involving the fractional 𝑝-Laplacian operator. By applying the linking theorem and the mountain pass theorem as well, the interaction of the nonlinearities with the first eigenvalue of the fractional 𝑝-Laplacian will be used to prove existence of multiple solutions.

中文翻译：

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分数 𝑝-拉普拉斯算子的临界凹凸 Ambrosetti-Prodi 类型问题

摘要 在本文中，我们考虑一类涉及分数 𝑝-拉普拉斯算子的临界凸凸 Ambrosetti-Prodi 类型问题。通过应用链接定理和山口定理，非线性与分数 𝑝-拉普拉斯算子的第一特征值的相互作用将用于证明多个解的存在。