Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions. (28th March 2020) - Yan, Dongliang
Abstract : We show the existence of positive solutions for a singular superlinear fourth-order equation with nonlinear boundary conditions. u ⁗ x = λ h x f u x, x ∈ 0, 1, u 0 = u ′ 0 = 0, u ″ 1 = 0, u ⁗ 1 + c u 1 u 1 = 0, where λ > 0 is a small positive parameter, f : 0, ∞ ⟶ ℝ is continuous, superlinear at ∞, and is allowed to be singular at 0, and h : [0, 1] ⟶ [0, ∞) is continuous. Our approach is based on the fixed-point result of Krasnoselskii type in a Banach space.