Existence and localization of solutions for fourth-order boundary-value problems
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In this paper, we study the existence of solutions for the differential equation
u(4)(t) = ƒ(t, u(t), u″(t)),
where ƒ 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.
CitationEnguiça, R., & Sanchez, L. (2007). Existence and localization of solutions for fourth-order boundary-value problems. Electronic Journal of Differential Equations, 2007(127), pp. 1-10.
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