Multiple solutions of inhomogeneous H-systems with zero Dirichlet boundary conditions

In this paper, we study the existence of multiple solutions to the Dirichlet problem of the inhomogeneous H-system:Δu=2Hu_xΛu_y+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 [16].