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One-dimensional nonlinear Laplacians under a 3-point boundary condition

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Abstract

We consider a three-point boundary value problem for operators such as the one-dimensional p-Laplacian, and show when they have solutions or not, and how many. The inverse operators are given by various formulas involving zeros of a real-valued function. They are shown to be order-preserving, for some parameter values, and non-singleton valued for others. The operators are shown to be m-dissipative in the space of continuous functions.

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  1. Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand

    Bruce D. Calvert

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  1. Bruce D. Calvert
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Correspondence to Bruce D. Calvert.

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Calvert, B.D. One-dimensional nonlinear Laplacians under a 3-point boundary condition. Acta. Math. Sin.-English Ser. 26, 1641–1652 (2010). https://doi.org/10.1007/s10114-010-7285-6

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  • DOI: https://doi.org/10.1007/s10114-010-7285-6

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