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In this paper we study the third-order nonlinear boundary value problem
(Φ(u''))'(t) + f(t, u(t), u'(t), u''(t)) = 0 a.e. t ∈ [0,1],
u(0) = 0, g(u'(0), u''(0)) = A, h(u'(1), u''(1)) = B,
where A, B ∈ ℝ, f : [0,1] × ℝ3 → ℝ is a Carathéodory function, g, h ∈ C0(ℝ2,ℝ) and Φ ∈ C0(ℝ, ℝ). Using apriori estimates, the Nagumo condition, upper and lower solutions and the Schauder fixed point theorem, we are able to prove existence of solutions of this problem.
Cite this article
De-Xiang Ma, Shu-Zhen Sun, Existence of solutions for a third-order boundary value problem with <var>p</var>-Laplacian operator and nonlinear boundary conditions. Port. Math. 66 (2009), no. 1, pp. 13–27DOI 10.4171/PM/1828