Existence and multiplicity of solutions for a Neumann problem involving the -Laplace operator

✍ Scribed by Lin-Lin Wang; Yong-Hong Fan; Wei-Gao Ge

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 595 KB
• Volume: 71
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2009.02.116

✦ Synopsis

In this paper, we study the following nonlinear Neumann boundary value problem

where Ω ⊂ R n is a bounded domain with smooth boundary ∂Ω, ∂u ∂v is the outer unit normal derivative on ∂Ω, λ > 0 is a real number, p is a continuous function on Ω with inf x∈Ω p(x) > 1, f : Ω × R → R is a continuous function. Using the three critical point theorem due to Ricceri, under the appropriate assumptions on f , we establish the existence of at least three solutions of this problem. Some known results are generalized.