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

In this paper, we study the existence of multiple solutions to the Dirichlet problem of the inhomogeneous H-system: View the MathML source where View the MathML source is a bounded smooth domain, H>0 a constant, and View the MathML source is a given function. By Ekelandʹs variational principle and the Mountain Pass Theorem, we prove that, for f≢0 satisfying some assumptions, the problem has at least two solutions in View the MathML source. This is not the case if f≡0 and Ω is simply-connected [16].