Advances in Differential Equations

Positive solutions of semilinear elliptic eigenvalue problems with concave nonlinearities

Kenichiro Umezu

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we prove the existence and nonexistence results for positive solutions to semilinear elliptic boundary value problems, with concave nonlinearities inside a smooth bounded domain and on the boundary. Our approach relies on sub and supersolutions, as well as the Nehari manifold that may contain the critical points for the energy functional associated with the boundary value problem. The fibering method helps us to study the properties of the Nehari manifold.

Article information

Source
Adv. Differential Equations Volume 12, Number 12 (2007), 1415-1436.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867408

Mathematical Reviews number (MathSciNet)
MR2382731

Zentralblatt MATH identifier
1180.35198

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J20: Variational methods for second-order elliptic equations 35J25: Boundary value problems for second-order elliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations 47J30: Variational methods [See also 58Exx] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

Umezu, Kenichiro. Positive solutions of semilinear elliptic eigenvalue problems with concave nonlinearities. Adv. Differential Equations 12 (2007), no. 12, 1415--1436. https://projecteuclid.org/euclid.ade/1355867408.


Export citation