April 2008
Electronic Journal of Differential Equations;2008, Vol. 2008, Special section p1
Academic Journal
In this paper, we show that for each &lambd; ∈ ℝ, there is an increasing sequence of eigenvalues for the nonlinear boundary-value problem Δpu = |u|p-2u in Ω |∇u|p-2 ∂u/∂v = λρ(x)|u|p-2u + μ|u|p-2u on ∂Ω; also we show that the first eigenvalue is simple and isolated. Some results about their variation, density, and continuous dependence on the parameter λ are obtained.


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