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Strong oscillation of elliptic systems of second order partial differential equations

Samuel M. Rankin — 1975

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Si dà una condizione sufficiente ad assicurare il carattere fortemente oscillatorio dei sistemi ellittici del tipo i , j = 1 n D i ( A i j ( x ) D j u ) + C ( x ) u = 0 . Con questo risultato si estendono vari criteri noti relativi al caso di una sola equazione.

On Fractional Helmholtz Equations

Samuel, M.Thomas, Anitha — 2010

Fractional Calculus and Applied Analysis

MSC 2010: 26A33, 33E12, 33C60, 35R11 In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox's H-function.

Oscillation of a forced nonlinear second order differential equation

Gary D. JonesSamuel M. Rankin — 1975

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Gli Autori considerano l'equazione y ′′ + p ( t ) g ( y ) = f ( t ) con p ( t ) , f ( t ) continue in [ 0 , ) , p ( t ) = 0 , g ( t ) continue in ( - , ) e sotto opportune condizioni per p ( t ) , g ( y ) , f ( t ) provano che tutte le soluzioni della (1) sono oscillanti.

On the first homology of Peano continua

Gregory R. ConnerSamuel M. Corson — 2016

Fundamenta Mathematicae

We show that the first homology group of a locally connected compact metric space is either uncountable or finitely generated. This is related to Shelah's well-known result (1988) which shows that the fundamental group of such a space satisfies a similar condition. We give an example of such a space whose fundamental group is uncountable but whose first homology is trivial, showing that our result does not follow from Shelah's. We clarify a claim made by Pawlikowski (1998) and offer a proof of the...

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