Remarks on semilinear problems with nonlinearities depending on the derivative
Almira, Jose Maria
Del Toro, Naira
Southwest Texas State University, Department of Mathematics
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.
Nonlinear boundary-value problem, Neumann and Periodic problems
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.