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Solitary Waves and Electromagnetic Fields

Donato Fortunato — 2008

Bollettino dell'Unione Matematica Italiana

Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localized packet; by soliton, we mean a solitary wave which exhibits some form of stability. In this respect solitary waves and solitons have a particle-like behavior and they occur in many questions of mathematical physics, such as superconductivity, phase transition, classical and quantum field theory, non linear optics, (see e.g. [37], [50], [56]). We are not interested in the study of a particular model....

Fourth-order nonlinear elliptic equations with critical growth

David E. EdmundsDonato FortunatoEnrico Jannelli — 1989

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

In this paper we consider a nonlinear elliptic equation with critical growth for the operator Δ 2 in a bounded domain Ω n . We state some existence results when n 8 . Moreover, we consider 5 n 7 , expecially when Ω is a ball in n .

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