On the eigenvalues of an elliptic operator
Sergio Campanato (1992)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Let be a bounded open convex set of class . Let be a non linear operator satisfying the condition (A) (elliptic) with constants , , . We prove that a number is an eigenvalue for the operator if and only if the number is an eigen-value for the operator . If , the two systems and have the same solutions. In particular, also the eventual eigen-values of the operator should all be negative. Finally, we obtain a sufficient condition for the existence of solutions ...