论文标题
一维非线性非局部问题的周期性解决方案，包括奇异非线性
Periodic solutions for one-dimensional nonlinear nonlocal problem with drift including singular nonlinearities
论文作者
论文摘要
In this paper, we prove existence results of a one-dimensional periodic solution to equations with the fractional Laplacian of order $s\in(1/2,1)$, singular nonlinearity, and gradient term under various situations, including nonlocal contra-part of classical Lienard vector equations, as well other nonlocal versions of classical results know only in the context of second-order ODE.我们的证明基于程度理论和Perron的方法，因此在此之前，我们需要在方程中出现的非线性假设下建立各种先验估计。此外，我们还获得了多重性在丢失先验界限并发生无限分叉的制度中。
In this paper, we prove existence results of a one-dimensional periodic solution to equations with the fractional Laplacian of order $s\in(1/2,1)$, singular nonlinearity, and gradient term under various situations, including nonlocal contra-part of classical Lienard vector equations, as well other nonlocal versions of classical results know only in the context of second-order ODE. Our proofs are based on degree theory and Perron's method, so before that we need to establish a variety of priori estimates under different assumptions on the nonlinearities appearing in the equations. Besides, we obtain also multiplicity results in a regime where a priori bounds are lost and bifurcation from infinity occurs.
