Positive radial solutions for p-Laplacian systems
نویسندگان
چکیده
The paper deals with the existence of positive radial solutions for the p-Laplacian system div(|∇ui| ∇ui) + f (u1, . . . , un) = 0, |x| < 1, ui(x) = 0, on |x| = 1, i = 1, . . . , n, p > 1, x ∈ R . Here f , i = 1, . . . , n, are continuous and nonnegative functions. Let u = (u1, . . . , un), ‖u‖ = ∑n i=1|ui|, f i 0 = lim‖u‖→0 f(u) ‖u‖p−1 , f i ∞ = lim‖u‖→∞ f(u) ‖u‖p−1 , i = 1, . . . , n, f = (f1, . . . , f), f0 = ∑n i=1 f i 0 and f∞ = ∑n i=1 f i ∞. We prove that f0 = ∞ and f∞ = 0 (sublinear), guarantee the existence of positive radial solutions for the problem. Our methods employ fixed point theorems in a cone.
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