Parameter dependence of solutions of classes of quasi-linear elliptic and parabolic differential equations

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.KeywordsMaximum PrinciplePositive MeasureTaylor Series ExpansionLower SolutionConvergent SequenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.