Discrete Elliptic Dirichlet Problems and Nonlinear Algebraic Systems

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• 作者：Maurizio Imbesi ; Giovanni Molica Bisci
• 关键词：39A10 ; 34B15 ; 35B38 ; Discrete nonlinear boundary value problems ; algebraic systems ; infinitely many solutions ; difference equations
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：13
• 期：1
• 页码：263-278
• 全文大小：568 KB
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• 作者单位：Maurizio Imbesi (1)
  Giovanni Molica Bisci (2)
  
  1. Department of Mathematics, University of Messina, Viale Ferdinando Stagno d’Alcontres, 3198166, Messina, Italy
  2. Dipartimento P.A.U, Università à degli Studi “Mediterranea” di Reggio Calabria, Salita Melissari-Feo di Vito, 89100, Reggio Calabria, Italy
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454

文摘

In this paper we are interested in the existence of infinitely many solutions for a partial discrete Dirichlet problem depending on a real parameter. More precisely, we determine unbounded intervals of parameters such that the treated problems admit either an unbounded sequence of solutions, provided that the nonlinearity has a suitable behaviour at infinity, or a pairwise distinct sequence of solutions that strongly converges to zero if a similar behaviour occurs at zero. Finally, the attained solutions are positive when the nonlinearity is supposed to be nonnegative thanks to a discrete maximum principle. Mathematics Subject Classification 39A10 34B15 35B38