An Existence Theorem for Quasilinear Systems
نویسنده
چکیده
This paper deals with the existence of positive radial solutions for the quasilinear system div(|∇ui|p−2∇ui) + λf (u1, . . . , un) = 0, |x| < 1, ui(x) = 0, on |x| = 1, i = 1, . . . , n, p > 1, λ > 0, x ∈ RN . The f i, i = 1, . . . , n, are continuous and non-negative functions. Let u = (u1, . . . , un), ‖u‖ = ∑n i=1 |ui|, f i 0 = lim ‖u‖→0 f i(u) ‖u‖p−1 , i = 1, . . . , n, f = (f1, . . . , fn), f0 = ∑n i=1 f i 0. We prove that the problem has a positive solution for sufficiently small λ > 0 if f0 = ∞. Our methods employ a fixed-point theorem in a cone.
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