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EXISTENCE RESULTS FOR POSITIVE SOLUTIONS OF NON-HOMOGENEOUS BVPS FOR SECOND ORDER DIFFERENCE EQUATIONS WITH ONE-DIMENSIONAL p-LAPLACIAN

Department of Mathematics
대한수학회 (The Korean Mathematical Society)|2010.01|대한수학회지 (Journal of the KMS)|제47권 제1호|pp. 135-163

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참고문헌

키워드

positive solutionone-dimension p-Laplacian difference equationmulti-point boundary value problem
주제분류수학

초록

Motivated by [Science in China (Ser. A Mathematics) 36(2006), no. 7, 721–732], this article deals with the following discrete type [수식]The sufficient conditions to guarantee the existence of at least three positive solutions of the above multi-point boundary value problem are established by using a new fixed point theorem obtained in [5]. An example is presented to illustrate the main result. 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 operator △x(n).

Abstract

Motivated by [Science in China (Ser. A Mathematics) 36(2006), no. 7, 721–732], this article deals with the following discrete type [수식]The sufficient conditions to guarantee the existence of at least three positive solutions of the above multi-point boundary value problem are established by using a new fixed point theorem obtained in [5]. An example is presented to illustrate the main result. 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 operator △x(n).

참고문헌 (18)

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  11. R. Leggett, "Multiple positive fixed points of nonlinear operators on ordered Banach spaces", Indiana Univ. Math. J., 28(4), pp.673~688 (1979)
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  13. H. Pang, "Multiple positive solutions of quasi-linear boundary value problems for finite difference equations", Appl. Math. Comput., 197(1), pp.451~456 (2008)
  14. P. J. Y.Wong, "Existence theorems for a system of difference equations with (n, p)-type conditions", Appl. Math. Comput., 123(3), pp.389~407 (2001)
  15. P. J. Y. Wong, "Three symmetric solutions of Lidstone boundary value problems for difference and partial difference equations", Comput. Math. Appl., 45(6), pp.1445~1460 (2003)
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