【摘 要】
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We consider the boundary value problem for the quasilinear equation div(A(|Du|)Du) + f(u) = 0, u ＞ 0, x ∈ BR(0), u| BR(0) = 0,where A and f are continuous funct
【机 构】
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Department of Mathematics, University of Science and Technology of China, Hefei 230026, Anhui, China
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We consider the boundary value problem for the quasilinear equation div(A(|Du|)Du) + f(u) = 0, u ＞ 0, x ∈ BR(0), u| BR(0) = 0,where A and f are continuous functions in (0, ∞) and f is positive in (0, 1), f(1) = 0.We prove that (1) if f is strictly decreasing, the problem has a unique classical radial solution for any real number R ＞ 0; (2) if f is not monotonous, the problem has at least one classical radial solution for some R ＞ 0 large enough.
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