A global bifurcation result of a Neumann problem with indefinite weight.
Boundary eigencurve problems involving the -Laplacian operator.
Existence and regularity of positive solutions for an elliptic system.
Bifurcation of nonlinear elliptic system from the first eigenvalue.
Stability of the principal eigenvalue of a nonlinear elliptic system.
Simplicity and stability of the first eigenvalue of a nonlinear elliptic system.
On the principal eigencurve of the p-Laplacian related to the Sobolev trace embedding
We prove that for any λ ∈ ℝ, there is an increasing sequence of eigenvalues μₙ(λ) for the nonlinear boundary value problem ⎧ in Ω, ⎨ ⎩ 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.
Page 1