Existence and location result for a fourth order boundary value problems

• Autor(a) principal: Santos, Ana I.
• Data de Publicação: 2005
• Outros Autores: Minhós, Feliz M., Gyulov, Thiomir
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10174/2714
• topic: fourth order BVP; Nagumo condition; a pair of lower and upper solutions; degree theory; a priori estimate

In the present work we prove an existence and location result for the fourth order fully nonlinear equation u^{(iv)}=f(t,u,u′,u′′,u′′′), 0<t<1, with the Lidstone boundary conditions u(0)=u′′(0)=u(1)=u′′(1)=0, where f:[0,1]×R⁴→R is a continuous function satisfying a Nagumo type condition. The existence of at least a solution lying between a pair of well ordered lower and upper solutions is obtained using an a priori estimates, lower and upper solutions method and degree theory.