Various Half-Eigenvalues of Scalar p-Laplacian with Indefinite Integrable Weights

Abstract EN

Consider the half-eigenvalue problem (ϕp(x′))′+λa(t)ϕp(x+)−λb(t)ϕp(x−)=0 a.e.

t∈[0,1], where 1

We characterize the spectra structure under periodic, antiperiodic, Dirichlet, and Neumann boundary conditions, respectively.

Furthermore, all these half-eigenvalues are continuous in (a,b)∈(ℒγ,wγ)2, where wγ denotes the weak topology in ℒγ space.

The Dirichlet and the Neumann half-eigenvalues are continuously Fréchet differentiable in (a,b)∈(ℒγ,∥⋅∥γ)2, where ∥⋅∥γ is the Lγ norm of ℒγ.