On the antimaximum principle for the discrete p-Laplacian with sign-changing weight

Hamza Chehabi, Omar Chakrone and Mohammed Chehabi

Applied Mathematics and Computation, 2019, vol. 342, issue C, 112-117

Abstract: This work deals with the antimaximum principle for the discrete Neumann and Dirichlet problem −Δφp(Δu(k−1))=λm(k)|u(k)|p−2u(k)+h(k)in[1,n].We prove the existence of three real numbers 0 ≤ a < b < c such that, if λ ∈ ]a, b[, every solution u of this problem is strictly positive (maximum principle), if λ ∈ ]b, c[, every solution u of this problem is strictly negative (antimaximum principle) and if λ=b, the problem has no solution. Moreover these three real numbers are optimal.

Keywords: Difference equations; Discrete p-Laplacian; Maximum principle; Antimaximum principle; Eigenvalue; Eigenfunction (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:342:y:2019:i:c:p:112-117

DOI: 10.1016/j.amc.2018.09.012

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