Existence of infinitely many solutions of a beam equation with non-monotone nonlinearity. (February 2017)

• Record Type: Journal Article
• Authors: Chen, Shaowei; Xu, Hai
• Is Part Of: Nonlinear analysis. Volume 33(2017)
• Page Start: 181
• Page End: 199
• Publication Date: 2017-02
• Subjects: Critical point theory -- Nonlinear beam equation -- Infinitely many solutions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.06.010
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we prove a new critical point theorem without the ( PS ) ∗ condition or the ( WPS ) ∗ condition. Using this theorem, we prove the existence of infinitely many solutions of the following sublinear beam equation { u t t + u x x x x + f ( x, t, u ) = 0 for ( x, t ) ∈ Q = ( 0, π ) × ( 0, 2 π ) u ( 0, t ) = u ( π, t ) = u x x ( 0, t ) = u x x ( π, t ) for t ∈ R u ( x, t ) = u ( t + 2 π, x ) for t ∈ ( 0, π ) × R . Unlike the previous results on this equation, we do not impose any monotone conditions on the variable ξ in the nonlinearity f ( x, t, ξ ) .