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

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  • Chehabi, Hamza
  • Chakrone, Omar
  • Chehabi, Mohammed

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.

Suggested Citation

  • Chehabi, Hamza & Chakrone, Omar & Chehabi, Mohammed, 2019. "On the antimaximum principle for the discrete p-Laplacian with sign-changing weight," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 112-117.
    • Handle: RePEc:eee:apmaco:v:342:y:2019:i:c:p:112-117
    DOI: 10.1016/j.amc.2018.09.012
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    Cited by:

    1. Kim, Jong-Ho & Park, Jea-Hyun, 2020. "Complete characterization of flocking versus nonflocking of Cucker–Smale model with nonlinear velocity couplings," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).

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