Summary
The question of polar instability of spherical shells due to core magnetic polarization examined briefly in a preceding communication is treated in more detail regarding Dirac's theory of magnetic charges and physical solutions of differential equations of Abel type resulting from the demand of rotational invariance. Both localized approximate solutions and several singular solutions or quasi-solutions with physical appeal are proposed, for the deformed spherical shell.
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References
J.-P. M. Lebrun:Lett. Nuovo Cimento,31, 390 (1980);34, 413 (1982);Nuovo Cimento A,99, 211 (1988).
J.-P. M. Lebrun:Lett. Nuovo Cimento,39, 257 (1984).
J.-P. M. Lebrun:Nuovo Cimento A,101, 515 (1989).
General references on differential equations:A. R. Forsyth:A Theory of Differential Equations (3 vols.) (Cambridge University, reprint by Dover, N.Y.);E. Goursat:Analyse mathématique, Vol.2, part 2 (differential equations) (Cambridge University, reprint by Dover, N. Y.);V. Nemitzkii andV. Stepanov:Qualitative Theory of Differential Equations (Princeton University Press, Princeton, N. J., 1960);R. Bellman:Stability Theory of Differential Equations (London, 1953, reprint by Dover, New York, N.Y.).
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5, rue d'Egmont, 1050 Bruxelles.
Institut de Physique, B-5, B-4000 Sart-Tilman (Liège).
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Lebrun, J.P.M. On two coupled Abel-type differential equations arising in a magnetostatic problem. Nuov Cim A 103, 1369–1379 (1990). https://doi.org/10.1007/BF02820566
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DOI: https://doi.org/10.1007/BF02820566