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

G.A. Afrouzi and S.H. Rasouli

Chaos, Solitons & Fractals, 2006, vol. 29, issue 5, 1095-1099

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).

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:29:y:2006:i:5:p:1095-1099

DOI: 10.1016/j.chaos.2005.08.165

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