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Sull'esistenza dell'unica soluzione di una certa equazione lineare a derivate parziali del primo ordine

Mauro Picone — 1973

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

In a previous paper I have proved the unicity of the solution of a certain linear partial differential equation of the first order. Here I give sufficient conditions for the existence and calculability of such a solution; moreover, I transform the above equation into a linear integral equation of a new type.

Su un teorema della teoria delle equazioni lineari a derivate parziali del primo ordine

Mauro Picone — 1972

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

A first order linear partial differential equation is considered in an interval T of the r-dimensional cartesian space. Under suitable hypotheses it is shown that this equation has at most one smooth solution in T. This result generalizes to an arbitrary r a theorem given by the author, since 1930, in the case r = 2.

Sugli intervalli oscillatorii di alcune variabili reali ordinate

Mauro Picone — 1971

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

In considering a pair of ordered real variables (such as appears in fundamental chapters of most treatises of infinitesimal analysis), it is shown that the oscillation interval of one of the two variables is always completely contained in the oscillation interval of the other variable.

Un apporto alla fenomenologia delle equazioni lineari a derivate parziali

Mauro Picone — 1971

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

A simple unprecedented example is given concerning a linear partial differential equation of an arbitrary order in two real independent variables, a solution of which is determined in a suitably given domain, when its value along an arc lying in it is prescribed.

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