Solvability for a third order discontinuous fully equation with nonlinear functional boundary conditions
We prove an existence and location result for the third order functional nonlinear boundary value problem u′′′(t) = f(t,u,u′(t),u′′(t)), for t∈[a,b], 0 = L₀(u,u′,u(t₀)), 0 = L₁(u,u′,u′(a),u′′(a)), 0 = L₂(u,u′,u′(b),u′′(b)), with t₀∈[a,b] given, f:I×C(I)×R²→R is a L¹- Carathéodory function allowing s...
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| Outros Autores: | , |
| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2011
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| Assuntos: | |
| Texto completo: | http://hdl.handle.net/10174/2715 |
| País: | Portugal |
| Oai: | oai:dspace.uevora.pt:10174/2715 |
| Resumo: | We prove an existence and location result for the third order functional nonlinear boundary value problem u′′′(t) = f(t,u,u′(t),u′′(t)), for t∈[a,b], 0 = L₀(u,u′,u(t₀)), 0 = L₁(u,u′,u′(a),u′′(a)), 0 = L₂(u,u′,u′(b),u′′(b)), with t₀∈[a,b] given, f:I×C(I)×R²→R is a L¹- Carathéodory function allowing some discontinuities on t and L₀,L₁, L₂ are continuous functions depending functionally on u and u′. The arguments make use of an a priori estimate on u′′, lower and upper solutions method and degree theory. Applications to a multipoint problem and to a beam equation will be presented. |
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