Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 69, pp. 1-9.
Title: A fibering map approach to a semilinear elliptic boundary value problem
Authors: Kenneth J. Brown (Heriot-Watt Univ., Riccarton, UK)
Tsung-Fang Wu (National Univ. of Kaohsiung, Taiwan)
Abstract:
We prove the existence of at least two positive solutions for
the semilinear elliptic boundary-value problem
$$
-\Delta u(x) = \lambda a(x) u^q + b(x) u^p \quad\mbox{for } x \in \Omega;
\quad u(x) = 0 \quad \mbox{for } x \in \partial \Omega
$$
on a bounded region $\Omega$ by using the Nehari manifold and
the fibering maps associated with the Euler functional for the problem.
We show how knowledge of the fibering maps for the problem leads to
very easy existence proofs.
Submitted February 27, 2007. Published May 10, 2007.
Math Subject Classifications: 35J20, 36J65.
Key Words: Semilinear elliptic boundary value problem;
variational methods; Nehari manifold; fibering map.