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A two-point boundary value problem with jumping nonlinearities

Author: Alfonso Castro B.
Journal: Proc. Amer. Math. Soc. 79 (1980), 207-211
MSC: Primary 34B10
MathSciNet review: 565340
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Abstract: We prove that a certain two point BVP with jumping nonlinearities has a solution. Our result generalizes that of [2]. We use variational methods which permit giving a minimax characterization of the solution. Our proof exposes the similarities between the variational behavior of this problem and that of other semilinear problems with noninvertible linear part (see [5]).

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  • [2] L. Aguinaldo and K. Schmitt, On the boundary value problem $ u'' + u = \alpha {u^ - } + p(t),u(0) = 0 = u(\pi )$, Proc. Amer. Math. Soc. 68 (1978), 64-68. MR 0466707 (57:6584)
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Keywords: Critical point, weak solution, jumping nonlinearities
Article copyright: © Copyright 1980 American Mathematical Society

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