Abstract
In this paper, we prove that if Q and f satisfy some suitable conditions, then - Δ u + u = Q (x) f (u) in R+N with the boundary condition u (y, 0) = λ g (y) has at least two positive solutions if 0 < λ < λ*, a unique positive solution if λ = λ* and no positive solution if λ > λ*.
Original language | English |
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Pages (from-to) | 849-865 |
Number of pages | 17 |
Journal | Nonlinear Analysis, Theory, Methods and Applications |
Volume | 70 |
Issue number | 2 |
DOIs | |
State | Published - 15 01 2009 |
Keywords
- Boundary value problems
- Multiple positive solutions
- Semilinear elliptic
- The half space