We prove the existence of at least two positive solutions for the semilinear elliptic boundary-value problem - ?u(x) = ?a(x)u q + b(x)up for x ?O; u(x) = 0 for x ? ?O on a bounded region O 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. © 2007 Texas State University.
|Number of pages||9|
|Journal||Electronic Journal of Differential Equations|
|Publication status||Published - 10 May 2007|
- Fibering map
- Nehari manifold
- Semilinear elliptic boundary value problem
- Variational methods