In this paper, we study the existence of multiple solutions to the Dirichlet problem of the inhomogeneous H-system:Δu=2HuxΛuy+finΩ,u|∂ Ω=0,where Ω⊂R2 is a bounded smooth domain, H > 0 a constant, and f ∈ H-1(Ω;R3) is a given function. By Ekeland's variational principle and the Mountain Pass Theorem, we prove that, for f≢0 satisfying some assumptions, the problem has at least two solutions in H01(Ω;R3). This is not the case if f≡0 and Ω is simply-connected .
|Number of pages||21|
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - Jan 2003|
All Science Journal Classification (ASJC) codes
- Applied Mathematics