Global solution curves for a class of elliptic systems |
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Authors: | Philip Korman |
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Institution: | 1. Department of Mathematical Sciences , University of Cincinnati , Cincinnati, OH 45221-0025, USA kormanp@math.uc.edu |
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Abstract: | We study curves of positive solutions for a system of elliptic equations of Hamiltonian type on a unit ball. We give conditions for all positive solutions to lie on global solution curves, allowing us to use the analysis similar to the case of one equation, as developed in P. Korman, Y. Li and T. Ouyang An exact multiplicity result for a class of semilinear equations, Commun. PDE 22 (1997), pp. 661–684.] (see also T. Ouyang and J. Shi Exact multiplicity of positive solutions for a class of semilinear problems, II, J. Diff. Eqns. 158(1) (1999), pp. 94–151].). As an application, we obtain some non-degeneracy and uniqueness results. For the one-dimensional case we also prove the positivity for the linearized problem, resulting in more detailed results. |
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Keywords: | elliptic systems global solution curves uniqueness and non-degeneracy of solutions |
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