The third order spectrum of the p-biharmonic operator with weight
We show that the spectrum of , where , under Navier boundary conditions, contains at least one sequence of eigensurfaces.
Boundary eigencurve problems involving the biharmonic operator
The aim of this paper is to study the spectrum of the fourth order eigenvalue boundary value problem ⎧Δ²u = αu + βΔu in Ω, ⎨ ⎩u = Δu = 0 on ∂Ω. where (α,β) ∈ ℝ². We prove the existence of a first nontrivial curve of this spectrum and we give its variational characterization. Moreover we prove some properties of this curve, e.g., continuity, convexity, and asymptotic behavior. As an application, we study the non-resonance of solutions below...
Three solutions for a nonlinear Neumann boundary value problem
The aim of this paper is to establish the existence of at least three solutions for the nonlinear Neumann boundary-value problem involving the p(x)-Laplacian of the form in Ω, on ∂Ω. Our technical approach is based on the three critical points theorem due to Ricceri.
On the spectrum of the -Laplacian operator for Neumann eigenvalue problems with weights.
A generalization of Ekeland's variational principle with applications.
Note on the nodal line of the -Laplacian.
Existence of solutions for an eigenvalue problem with weight.
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