Isoperimetric inequalities for a nonlinear eigenvalue problem-Reference-Cited by-同舟云学术

Isoperimetric inequalities for a nonlinear eigenvalue problem

Published:1976 Issue:1 Volume:56 Page:243-246
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Bandle Catherine

Abstract

An estimate for the spectrum of the two-dimensional eigenvalue problem Δ u + λ e u = 0 \Delta u + \lambda {e^u} = 0 in D ( λ > 0 ) , u = 0 D(\lambda > 0),u = 0 on ∂ D \partial D is derived, and upper and lower pointwise bounds for the solutions are constructed.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1976-056-01/S0002-9939-1976-0477402-7/S0002-9939-1976-0477402-7.pdf

Reference6 articles.

1. Existence theorems, qualitative results and a priori bounds for a class of nonlinear Dirichlet problems;Bandle, Catherine;Arch. Rational Mech. Anal.,1975

2. Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems;Crandall, Michael G.;Arch. Rational Mech. Anal.,1975

3. Some problems in the theory of quasi-linear equations;Gel′fand, I. M.;Uspehi Mat. Nauk,1959

4. Some positone problems suggested by nonlinear heat generation;Keller, Herbert B.;J. Math. Mech.,1967

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