Remarks on semilinear problems with nonlinearities depending on the derivative

Date

2003-02-20

Authors

Almira, Jose Maria
Del Toro, Naira

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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.

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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.

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Attribution 4.0 International

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