Abstract
Earlier work, on the dependence of solutions of certain classes of quasi-linear elliptic and parabolic differential equations on embedded parameters, is extended and generalized. In particular, generic classes of linearly perturbed, and inhomogeneously perturbed, quasi-linear elliptic and parabolic boundary values problems whose stable positive solutions are Laplace transforms of positive measures, are identified. For a particular class of such problems the conjecture that the solution is a Stieltjes transform of a positive measure is explored. It is shown that low order rational fraction Padé approximants provide useful bounds, independently of whether or not the conjecture itself is true.
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References
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© 1980 Springer-Verlag
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Barnsley, M.F. (1980). Parameter dependence of solutions of classes of quasi-linear elliptic and parabolic differential equations. In: Bardos, C., Lasry, J.M., Schatzman, M. (eds) Bifurcation and Nonlinear Eigenvalue Problems. Lecture Notes in Mathematics, vol 782. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090425
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DOI: https://doi.org/10.1007/BFb0090425
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