We prove that for any λ ∈ ℝ, there is an increasing sequence of eigenvalues μₙ(λ) for the nonlinear boundary value problem ⎧ $Δₚu = |u|^{p-2}u$ in Ω, ⎨ ⎩ $|∇u|^{p-2} ∂u/∂ν = λϱ(x)|u|^{p-2}u + μ|u|^{p-2}u$ on crtial ∂Ω and we show that the first one μ₁(λ) is simple and isolated; we also prove some results about variations of the density ϱ and the continuity with respect to the parameter λ.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
In this paper, we study the spectrum for the following eigenvalue problem with the p-biharmonic operator involving the Hardy term: $Δ(|Δu|^{p-2} Δu) = λ(|u|^{p-2}u)/(δ(x)^{2p})$ in Ω, $u ∈ W₀^{2,p}(Ω)$. By using the variational technique and the Hardy-Rellich inequality, we prove that the above problem has at least one increasing sequence of positive eigenvalues.
3
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
We study the existence of solutions for a p-biharmonic problem with a critical Sobolev exponent and Navier boundary conditions, using variational arguments. We establish the existence of a precise interval of parameters for which our problem admits a nontrivial solution.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.