We consider a nonlinear boundary value problem with degenerate nonlocal term depending on the L q -norm of the solution and the p -Laplace operator. We prove the multiplicity of positive solutions for the problem, where the number of solutions doubles the number of “positive bumps” of the degenerate term. The solutions are also ordered according to their L q -norms.

中文翻译：

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具有 p-拉普拉斯算子的退化非局部问题的正解的多重性

我们考虑具有退化非局部项的非线性边值问题，这取决于解的 L q -范数和 p -Laplace 算子。我们证明了该问题的正解的多重性，其中解的数量是退化项的“正凸点”数量的两倍。解也根据它们的 L q 范数排序。