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Studies on Nonhomogeneous Multi-point BVPs of Difference Equations with One-Dimensional p-Laplacian

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Abstract

This article deals with a discrete type multi-point BVP of difference equations. The sufficient conditions to guarantee the existence of at least three positive solutions are established. An example is presented to illustrate the main results. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multifixed-point theorems can be extended to treat nonhomogeneous BVPs. The emphasis is put on the nonlinear term f involved with the first order delta operators Δx(n) and Δx(n + 1). The difference concerned is a implicit difference equation.

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Authors and Affiliations

  1. Department of Mathematics, Guangdong University of Business Studies, Guangzhou, 510000, P.R. China

    Yuji Liu

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  1. Yuji Liu
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Correspondence to Yuji Liu.

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Supported by Natural Science Foundation of Guangdong Province (No:7004569) and Natural Science Foundation of Hunan province, P.R.China(No:06JJ5008).

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Liu, Y. Studies on Nonhomogeneous Multi-point BVPs of Difference Equations with One-Dimensional p-Laplacian. Mediterr. J. Math. 8, 577–602 (2011). https://doi.org/10.1007/s00009-010-0089-1

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  • DOI: https://doi.org/10.1007/s00009-010-0089-1

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