Systems of coupled clamped beams equations with full nonlinear terms: Existence and location results

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• 作者：Feliz Minhó ; s^a ; ^{fminhos@uevora.pt} ; Infeliz Coxe^b ; ^{m82infelizcoxe@yahoo.com.br}
• 关键词：Coupled systems ; Green functions ; Nagumo-type condition ; Coupled lower and upper solutions ; Coupled clamped beams
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：35
• 期：Complete
• 页码：45-60
• 全文大小：787 K
• 卷排序：35

文摘

This work gives sufficient conditions for the solvability of the fourth order coupled system {u(4)(t)=f(t,u(t),u′(t),u″(t),u‴(t),v(t),v′(t),v″(t),v‴(t))v(4)(t)=h(t,u(t),u′(t),u″(t),u‴(t),v(t),v′(t),v″(t),v‴(t)) with f,h:[0,1]×R8→Rf,h:[0,1]×R8→R some L1L1- Carathéodory functions, and the boundary conditions {u(0)=u′(0)=u″(0)=u″(1)=0v(0)=v′(0)=v″(0)=v″(1)=0.To the best of our knowledge, it is the first time in the literature where two beam equations are considered with full nonlinearities, that is, with dependence on all derivatives of uu and vv.An application to the study of the bending of two elastic coupled clamped beams is considered.