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On constant-sign solutions of a system of discrete equations

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Abstract

We consider the following system of discrete equations

$$u_i (k) = \sum\limits_{\ell = 0}^N {g_i (k,\ell )fi(\ell ,u_1 (\ell )} ,u_2 (\ell ), \cdots ,u_n (\ell )), k \in \{ 0,1, \cdots ,T\} ,$$

1≤i≤n whereT≥N>0, 1≤i≤n. Existence criteria for single, double and multiple constant-sign solutions of the system are established. To illustrate the generality of the results obtained, we include applications to several well known boundary value problems. The above system is also extended to that on {0, 1,…}

$$u_i (k) = \sum\limits_{\ell = 0}^\infty {g_i (k,\ell )fi(\ell ,u_1 (\ell )} ,u_2 (\ell ), \cdots ,u_n (\ell )), k \in \{ 0,1, \cdots \} ,1 \leqslant i \leqslant n$$

for which the existence of constant-sign solutions is investigated.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Florida Institute of Technology, 32091-6975, Melbourne, FL, U.S.A.

    Ravi P. Agarwal

  2. Department of Mathematics, National University of Ireland, Galway, Ireland

    Donal O'Regan

  3. School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore, Singapore

    Patricia J. Y. Wong

Authors
  1. Ravi P. Agarwal
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  2. Donal O'Regan
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  3. Patricia J. Y. Wong
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Correspondence to Ravi P. Agarwal.

Additional information

Ravi P. Agarwal, after receiving Ph.D. in 1973 from the Indian Institute of Technology, Madras, I served at REC, Tiruchirapalli and MATSCIENCE, Madras. Before the present appointment at the National University of Singapore I have spent two years at der Ludwig-Maximilians-Universität, Munich as an Alexander von Humboldt Foundation Fellow, and one year at Universitá, degli Dtudi, Florence as a Visiting Professor of Mathematics. My research interests focus on Differential and Difference Equations, Numerical Analysis and Inequalities. I have published over 400 research papers, 15 research monographs, and either an editor or an associate editor of 30 Journals and book series.

Donal O'Regan is a Lecturer of Mathematics at the National University of Ireland, Galway. He is the author of six books and has published over 200 research papers on fixed point theory; operator, integral, differential and difference equations; and nonlinear analysis. In addition he is assistant editor ofNonlinear Analysis and is on the editorial board of six other journals.

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Agarwal, R.P., O'Regan, D. & Wong, P.J.Y. On constant-sign solutions of a system of discrete equations. JAMC 14, 1–37 (2004). https://doi.org/10.1007/BF02936096

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  • DOI: https://doi.org/10.1007/BF02936096

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