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

✍ Scribed by Futoshi Takahashi

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 187 KB
• Volume: 52
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00108-6

✦ Synopsis

In this paper, we study the existence of multiple solutions to the Dirichlet problem of the inhomogeneous H-system:

where ⊂ R 2 is a bounded smooth domain, H ¿ 0 a constant, and f ∈ H -1 ( ; R 3 ) 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 H 1 0 ( ; R 3 ). This is not the case if f ≡ 0 and is simply-connected [16].