Nontrivial solution for a three-point boundary-value problem
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In this paper, we study the existence of nontrivial solutions for the second-order three-point boundary-value problem
u'' + ƒ(t, u) = 0, 0 < t < 1,
u'(0) = 0, u(1) = ɑu'(η).
where η ∈ (0, 1), ɑ ∈ ℝ, ƒ ∈ C([0, 1] x ℝ, ℝ). Under certain growth conditions on the nonlinearity ƒ and by using Leray-Schauder nonlinear alternative, sufficient conditions for the existence of nontrivial solution are obtained. We illustrate the results obtained with some examples.
CitationSun, Y. P. (2004). Nontrivial solution for a three-point boundary-value problem. Electronic Journal of Differential Equations, 2004(111), pp. 1-10.
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