Abstract:In this paper, we prove existence results of a one-dimensional periodic solution to equations with the fractional Laplacian of order s ∈ (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 d… Show more
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