论文标题
针对不对称反应的分数p拉平方程的四种溶液
Four solutions for fractional p-Laplacian equations with asymmetric reactions
论文作者
论文摘要
我们考虑了由退化的分数p-laplacian驱动的非线性，非局部方程的Dirichlet类型问题，该反应根据正参数和非对称扰动（在正线性的正线性，在负无度处为正性无限），其反应结合了sublinear术语。通过临界点理论和摩尔斯理论，我们证明，对于参数的足够小值，此类问题至少承认了四种非平凡的解决方案：两种正，一个负，一个nodal。作为工具，我们证明了Brezis-Oswald类型的比较结果。
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.
