Almira, Jose MariaDel Toro, Naira2020-09-142020-09-142003-02-20Almira, J. M., & Del Toro, N. (2003). Remarks on semilinear problems with nonlinearities depending on the derivative. <i>Electronic Journal of Differential Equations, 2003</i>(18), pp. 1-11.1072-6691https://hdl.handle.net/10877/12609In this paper, we continue some work by Cañada and Drábek [1] and Mawhin [6] on the range of the Neumann and Periodic boundary value problems: u''(t) + g(t, u'(t)) = f̄ + f̃(t), t ∈ (a, b) u'(a) = u'(b) = 0 or u(a) = u(b), u'(a) = u'(b) where g ∈ C ([a, b] x ℝn, ℝn), f̄ ∈ ℝn, and f̃ has mean value zero. For the Neumann problem with n > 1, we prove that for a fixed f̃ the range can contain an infinity continuum. For the one dimensional case, we study the asymptotic behavior of the range in both problems.Text11 pages1 file (.pdf)enAttribution 4.0 InternationalNonlinear boundary-value problemNeumann and Periodic problemsArticle