A note on a class of problems for a higher-order fully nonlinear equation under one-sided Nagumo-type condition

• Autor(a) principal: Santos, Ana I.
• Data de Publicação: 2009
• Outros Autores: Grossinho, Maria R., Minhós, Feliz M.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10174/2716
• topic: Higher order BVP; one-sided Nagumo-type conditions; lower and upper solutions; Leray-Schauder degree; a priori estimates

The purpose of this work is to establish existence and location results for the higher order fully nonlinear differential equation u⁽ⁿ⁾(t)=f(t,u(t),u′(t),…,u⁽ⁿ⁻¹⁾(t)), n≥2, with the boundary conditions u^{(i)}(a) = A, for i=0,⋯,n-3, u⁽ⁿ⁻¹⁾(a) = B, u⁽ⁿ⁻¹⁾(b)=C or u^{(i)}(a)=A, for i=0,⋯,n-3, c₁u⁽ⁿ⁻²⁾(a)-c₂u⁽ⁿ⁻¹⁾(a)=B, c₃u⁽ⁿ⁻²⁾(b)+c₄u⁽ⁿ⁻¹⁾(b)=C, with A_{i},B,C∈R, for i=0,⋯,n-3, and c₁, c₂, c₃, c₄ real positive constants. It is assumed that f:[a,b]×Rⁿ⁻¹→R is a continuous function satisfying one-sided Nagumo-type conditions which allows an asymmetric unbounded behavior on the nonlinearity. The arguments are based on Leray-Schauder topological degree and lower and upper solutions method.