Remarks on semilinear problems with nonlinearities depending on the derivative
Date
2003-02-20
Authors
Almira, Jose Maria
Del Toro, Naira
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
Nonlinear boundary-value problem, Neumann and Periodic problems
Citation
Almira, 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.