In this paper we develop a general technique for establishing analyticity of solutions of partial differential equations which depend on a parameter ε ε . The technique is worked out primarily for a free boundary problem describing a model of a stationary tumor. We prove the existence of infinitely many branches of symmetry-breaking solutions which bifurcate from any given radially symmetric steady state; these asymmetric solutions are analytic jointly in the spatial variables and in ε ε .
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Friedman et al. (2000) studied this question.
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