JournalsjemsVol. 8 , No. 2DOI 10.4171/jems/47

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

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.