Multiple sign changing solutions for a fourth-order elastic beam equation

Abstract Note: Please see pdf for full abstract with equations. The aim of the present paper is to investigate the existence of multiple positive, multiple negative, and in particular, of multiple sign changing solutions depending on λ for the following fourth-order problem uiv + Au''+ Bu = λƒ(t, u) in (0,1) u(0) = u(1) = 0 u''(0) = u''(1) = 0, where ƒ : [0,1] × R → R is a function, A and B are real constants and λ is a positive parameter. The nonlinearity ƒ is required to have an oscillatory behaviour. AMS subject classification: 34B15, 58E05.