On the principal eigenvalue of elliptic operators in $\R^N$ and applications

• Autores: Henri Berestychi, Luca Rossi
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 8, Nº 2, 2006, págs. 195-215
• Idioma: inglés
• DOI: 10.4171/jems/47
• Texto completo no disponible (Saber más ...)
• Resumen

  • Two generalizations of the notion of principal eigenvalue for elliptic operators in $\R^N$ are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and ``limit periodic'' operators. These results apply to questions of existence and uniqueness for some semi-linear problems in all of space. We also indicate several outstanding open problems and formulate some conjectures.