On a Fourth-Order Boundary Value Problem at Resonance. (11th June 2017)

• Record Type: Journal Article
• Authors: Xu, Man; Ma, Ruyun
• Other Names: Infante Gennaro Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2017(2017)
• Publication Date: 2017-06-11
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2017/2641856
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We investigate the spectrum structure of the eigenvalue problem u 4 x = λ u x, x ∈ 0, 1 ; u 0 = u 1 = u ′ 0 = u ′ 1 = 0 . As for the application of the spectrum structure, we show the existence of solutions of the fourth-order boundary value problem at resonance - u 4 x + λ 1 u x + g x, u x = h x, x ∈ 0, 1 ; u 0 = u 1 = u ′ 0 = u ′ 1 = 0, which models a statically elastic beam with both end-points being cantilevered or fixed, where λ 1 is the first eigenvalue of the corresponding eigenvalue problem and nonlinearity g may be unbounded.