Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions. (28th March 2020)

• Record Type: Journal Article
• Authors: Yan, Dongliang
• Other Names: Infante Gennaro Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-03-28
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/7308025
• Languages: English
• ISSNs: 2314-8896

Abstract

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.