Bounded solutions for a forced bounded oscillator without friction

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Soave, Nicola^1,2  Verzini, Gianmaria³ 

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20126 Milan, Italy

[2] Univ Picardie Jules Verne, CNRS UMR 7352, LAMFA, F-80039 Amiens, France

[3] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

关键词: Landesman-Lazer conditions;    Critical point theory;    Subharmonic solutions to periodic ODEs;    Ambrosetti-Prodi problems;   

DOI  :  10.1016/j.jde.2014.01.015

来源: Elsevier

【 摘 要 】

Under the validity of a Landesman-Lazer type condition, we prove the existence of solutions bounded on the real line, together with their first derivatives, for some second order nonlinear differential equation of the form ii + g(u) = p(t), where the reaction term g is bounded. The proof is variational, and relies on a dual version of the Nehari method for the existence of oscillating solutions to superlinear equations. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free