Wyniki wyszukiwania

1

On the principal eigencurve of the p-Laplacian related to the Sobolev trace embedding

100%

El Khalil A., Ouanan M.

Applicationes Mathematicae

|

2005

|

tom 32

|

nr 1

1-16

EN

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

On the spectrum of the p-biharmonic operator involving p-Hardy's inequality

81%

El Khalil A., Morchid Alaoui M., Touzani A.

Applicationes Mathematicae

|

2014

|

tom 41

|

nr 2-3

239-246

EN

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

On the p-biharmonic operator with critical Sobolev exponent

81%

El Khalil A., Morchid Alaoui M., Touzani A.

Applicationes Mathematicae

|

2014

|

tom 41

|

nr 2-3

229-237

EN

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.

Ograniczanie wyników

3 Applicationes Mathematicae

3 El Khalil A.

2 Morchid Alaoui M.

2 Touzani A.

1 Ouanan M.

2 2014

1 2005

On the principal eigencurve of the p-Laplacian related to the Sobolev trace embedding

On the spectrum of the p-biharmonic operator involving p-Hardy's inequality

On the p-biharmonic operator with critical Sobolev exponent