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A geometric proof of the Kwong-McLeod uniqueness result. (English) Zbl 0779.35040
A geometric proof via trajectory analysis of an equivalent first-order ordinary system is given for the uniqueness of the positive radially symmetric solution of the problem \(-\Delta u=f(u)\) in \(B\), \(u|_{\partial B}=0\), where \(B\) is a ball in \(\mathbb{R}^ n\), \(n\geq 3\). The hypotheses on \(f\) are as in K. McLeod’s proof [Techn. Report, Dept. Math. Sci., Univ. Wisconsin-Milwaukee (1989)], generalizing results of C. V. Coffman [Arch. Rat. Mech. Anal. 46, 81-95 (1972; Zbl 0249.35029)], K. McLeod and J. Serrin [ibid. 99, 115-145 (1987; Zbl 0667.35023)] and M. K. Kwong [ibid. 105, No. 3, 243-266 (1989; Zbl 0676.35032)].

MSC:
35J60 Nonlinear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
35P05 General topics in linear spectral theory for PDEs
34B15 Nonlinear boundary value problems for ordinary differential equations
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