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Existence of positive radial solutions of Dirichlet problems for elliptic equations \(\Delta u+g(|X|) f(u)=0\) in annulus. (Chinese. English summary) Zbl 0961.35061

Summary: We study the existence of positive radial solutions of elliptic equations \(\Delta u+ g(|X|)f(u)= 0\) in annular domains, subject to Dirichlet boundary conditions. In this paper it is not required that \(\lim_{l\to 0} f(l)/l\), \(\lim_{l\to\infty} f(l)/l\) exist. Our work is an extension to C. V. Coffman and M. Marcus [Arch. Ration. Mech. Anal. 108, No. 4, 293-307 (1989; Zbl 0699.35092)] and Haiyan Wang [J. Differ. Equations 109, No. 1, 1-7 (1994; Zbl 0798.34030)].

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
34B15 Nonlinear boundary value problems for ordinary differential equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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