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On the monotonicity of the time-map. (English) Zbl 0673.34008
The authors deal with the equation \(\Delta u(x)+f(u(x))=0,\) \(| x| <R\) together with the boundary conditions \(\alpha u(x)-\beta du(x)/dn=0,\) \(| x| =R\), and investigate the monotonicity of the time map \(p\mapsto T(p)\), \(p=u(0)\) which plays an important role in the behaviour of radical solutions and in symmetry breaking.
Reviewer: E.Barvinek

MSC:
34A30 Linear ordinary differential equations and systems, general
34K05 General theory of functional-differential equations
35B32 Bifurcations in context of PDEs
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[1] \scP. Clement and G. Sweers, Existence and multiplicity results for a semilinear eigenvalue problem, preprint. · Zbl 0662.35045
[2] Smoller, J.; Wasserman, A., Existence, uniqueness, and nondegeneracy of positive solutions of semilinear elliptic equations, Comm. math. phys., 95, 129-159, (1984) · Zbl 0582.35046
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