论文标题
周期性分数Ambrosetti-prodi用于一维问题的漂移
Periodic fractional Ambrosetti-Prodi for one-dimensional problem with drift
论文作者
论文摘要
我们建立了Ambrosetti -prodi类型结果，以定期解决一维非线性问题，即漂移项和漂移 - 其主要操作员是（0,1）$的订单$ s \ in ofder laplacian。我们建立了解决方案存在和不存在的条件。存在结果的证明基于亚启动方法与拓扑度类型参数相结合。我们还建立了先验界限以获得多重性结果。我们还证明，在非线性的某些规律性假设下，即方程的解决方案是经典的，解决方案是$ c^{1，α} $。我们完成了获得具有单数非线性的分数laplacian问题的工作结果。特别是，我们与单数非线性建立了Ambrosetti-Prodi类型问题。
We establish Ambrosetti -Prodi type results for periodic solutions of one -dimensional nonlinear problems with drift term and drift -less whose principal operator is the fractional Laplacian of order $s\in(0,1)$. We establish conditions for the existence and nonexistence of solutions. The proofs of the existence results are based on the sub-supersolution method combined with topological degree type arguments. We also establish a priori bounds in order to get multiplicity results. We also prove that the solutions are $C^{1,α}$ under some regularity assumptions in the nonlinearities, that is, the solutions of equations are classical. We finish the work obtaining existence results for problems with the fractional Laplacian with singular nonlinearity. In particular, we establish an Ambrosetti-Prodi type problem with singular nonlinearities.
