JournalsjemsVol. 8, No. 2pp. 195–215

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

  • Henry Berestycki

    Ecole des hautes études en sciences sociales, Paris, France
  • Luca Rossi

    Università di Roma La Sapienza, Italy
On the principal eigenvalue of elliptic operators in $\R^N$ and applications cover
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Abstract

Two generalizations of the notion of principal eigenvalue for elliptic operators in RN\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.

Cite this article

Henry Berestycki, Luca Rossi, On the principal eigenvalue of elliptic operators in RN\R^N and applications. J. Eur. Math. Soc. 8 (2006), no. 2, pp. 195–215

DOI 10.4171/JEMS/47