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Stability properties of non-negative solutions to a non-autonomous p-Laplacian equation

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  • Afrouzi, G.A.
  • Rasouli, S.H.

Abstract

We study the stability of non-negative stationary solutions of-Δpu=λg(x,u),x∈Ω,Bu=0,x∈∂Ω,where Δp denotes the p-Laplacian operator defined by Δpz=div(∣∇z∣p−2∇z); p>2, Ω is a bounded domain in RN(N⩾1) with smooth boundary Bu(x)=αh(x)u+(1-α)∂u∂n where α∈[0,1],h:∂Ω→R+ with h=1 when α=1, λ>0, and g:Ω×[0,∞)→R is a continuous function. If g(x,u)/up−1 be strictly increasing (decreasing), we provide a simple proof to establish that every non-trivial non-negative solution is unstable (stable).

Suggested Citation

  • Afrouzi, G.A. & Rasouli, S.H., 2006. "Stability properties of non-negative solutions to a non-autonomous p-Laplacian equation," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1095-1099.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:5:p:1095-1099
    DOI: 10.1016/j.chaos.2005.08.165
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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(5), pages 687-698, October.
    3. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(3), pages 381-386, June.
    4. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(4), pages 525-537, August.
    5. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(2), pages 285-292, April.
    6. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    7. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(1), pages 151-159, February.
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    Cited by:

    1. Yang, Zuodong & Miao, Qing, 2009. "Bifurcation results to some quasilinear differential equation systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1914-1925.

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