Abstract
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.
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Imbesi, M., Bisci, G.M. Discrete Elliptic Dirichlet Problems and Nonlinear Algebraic Systems. Mediterr. J. Math. 13, 263–278 (2016). https://doi.org/10.1007/s00009-014-0490-2
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DOI: https://doi.org/10.1007/s00009-014-0490-2