Remarks on semilinear problems with nonlinearities depending on the derivative
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In this paper, we continue some work by Cañada and Drábek  and Mawhin  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.
CitationAlmira, J. M., & Del Toro, N. (2003). Remarks on semilinear problems with nonlinearities depending on the derivative. Electronic Journal of Differential Equations, 2003(18), pp. 1-11.
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