On the stability of nonnegative solutions to classes of p-Laplacian systems

G Afrouzi, Z Sadeghi
2008 UK World Journal of Modelling and Simulation   unpublished
The purpose of this paper is to investigate stability properties for non-trivial non-negative stationary solutions to the classes of systems of the form −− pi u i (x) = f i (u 1 , u 2 , ..., u n) x ∈ Ω, Bu i (x) = 0 x ∈ ∂Ω, where s denotes the s-Laplacian operator defined by s z := div(||z| s−2 z); s > 1, where Ω ⊂ R n (n ≥ 1) is a bounded domain having a smooth boundary Bz(x) = αh(x)z + (1 − α) ∂z ∂n where α ∈ [0, 1] is a constant, h : ∂Ω → R + is a smooth function with h ≡ 1 when α = 1, and f
more » ... 1 when α = 1, and f i ∈ C 1 [0, +∞) for i = 1, ..., n. Then we infer stability(instability) in the case when system is cooperative and strictly coupled (∂fi ∂uj ≥ 0, i j, n j=1,ji (∂fi ∂uj) 2 > 0) and competitive and strictly coupled (∂fi ∂uj ≤ 0, i j, n j=1,ji (∂fi ∂uj) 2 > 0).
fatcat:d3aixdvz3rghpkhs4vkwd6pvca