We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, whose reaction combines a sublinear term depending on a positive parameter and an asymmetric perturbation (superlinear at positive infinity, at most linear at negative infinity). By means of critical point theory and Morse theory, we prove that, for small enough values of the parameter, such problem admits at least four nontrivial solutions: two positive, one negative, and one nodal. As a tool, we prove a Brezis-Oswald type comparison result.

中文翻译：

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具有不对称反应的分数 p-拉普拉斯方程的四个解

我们考虑由退化分数p-拉普拉斯算子驱动的非线性非局部方程的狄利克雷类型问题，其反应结合了取决于正参数和不对称扰动的亚线性项（在正无穷大时超线性，在负无穷大时至多线性）。通过临界点理论和莫尔斯理论，我们证明，对于足够小的参数值，该问题至少有四个非平凡解：两个正解、一个负解和一个节点。作为工具，我们证明了 Brezis-Oswald 类型比较结果。