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- Title
On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of Non-Self-Adjoint Elliptic Operators.
- Authors
Pyatnitskii, A. L.; Shamaev, A. S.
- Abstract
The article concerns the study of conditions on the non-self-adjoint elliptic operator defined in the whole space <MATH>\mathbb R</MATH>n, ensuring the existence and uniqueness of a constant-sign eigenfunction tending to zero at infinity. We also study the asymptotics of the corresponding eigenvalue as the coefficient in the highest-order derivative of the operator tends to zero. The result is formulated in terms connected with the variational problem for the Lagrangian on one-dimensional trajectories in the space <MATH>\mathbb R</MATH>n. The explicit form of this Lagrangian is given in terms of the coefficients of the original operator.
- Subjects
EIGENFUNCTIONS; EIGENVALUES; ELLIPTIC operators; NONSELFADJOINT operators; ASYMPTOTES; LAGRANGIAN functions
- Publication
Journal of Mathematical Sciences, 2004, Vol 120, Issue 3, p1411
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1023/B:JOTH.0000016058.00000.92