Electron. J. Diff. Eqns., Vol. 2007(2007), No. 127, pp. 1-10.

Existence and localization of solutions for fourth-order boundary-value problems

Ricardo Enguiça, Luis Sanchez

Abstract:
In this paper, we study the existence of solutions for the differential equation
$$ u^{(4)}(t)=f\big(t,u(t),u''(t)\big), $$
where $f$ satisfies one-sided Lipschitz conditions with respect to $u$ and $u''$, with periodic conditions or boundary conditions from "simply supported" beam theory. We assume the existence of lower and upper solutions (well-ordered and in some cases reversely ordered) and we make use of a fourth-order linear differential operator factorization.

Submitted July 20, 2007. Published September 28, 2007.
Math Subject Classifications: 34B15, 34C25.
Key Words: Beam equation; fourth order boundary value problem; maximum principles; lower and upper solutions; reversed order.

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Ricardo Enguiça
Area Científica de Matemática
Instituto Superior de Engenharia de Lisboa
Rua Conselheiro Emídio Navarro, 1 - 1950-062 Lisboa, Portugal
email: rroque@dec.isel.ipl.pt
Luís Sanchez
Faculdade de Ciências da Universidade de Lisboa
Avenida Professor Gama Pinto 2, 1649-003 Lisboa, Portugal
email: sanchez@ptmat.fc.ul.pt

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