The $$\infty $$ ∞ -eigenvalue problem with a sign-changing weight

Eigenvalue problems with sign-changing coefficients

We consider a class of eigenvalue problems involving coefficients changing sign on the domain of interest. We describe the main spectral properties of these problems according to the features of the coefficients. Then, under some assumptions on the mesh, we explain how one can use classical finite element methods to approximate the spectrum as well as the eigenfunctions while avoiding spurious ...

Infinitely many solutions for a bi-nonlocal‎ ‎equation with sign-changing weight functions

In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.

On an eigenvalue problem with variable exponents and sign-changing potential

In this paper we study a non-homogeneous eigenvalue problem involving variable growth conditions and a sign-changing potential. We prove that any λ > 0 sufficiently small is an eigenvalue of the nonhomogeneous eigenvalue problem { −div(a(|∇u|)∇u) = λV(x)|u|q(x)−2u, in Ω, u = 0, on ∂Ω. The proofs of the main results are based on Ekeland’s variational principle.

An Existence Result for a Semipositone Problem with a Sign Changing Weight

where p > 0, c > 0, and λ > 0 are parameters and Ω is an open bounded region with boundary ∂Ω in class C2 in Rn for n ≥ 1. Here g :Ω→ R is a Cα function while h :Ω→ R is a nonnegative Cα function with ‖h‖∞ = 1. When p = 1, (1.1) arises in population dynamics where 1/λ is the diffusion coefficient and ch(x) represents the constant yield harvesting. In this case (p = 1), when g(x) is a positive c...

Global Structure of Positive Solutions of a Discrete Problem with Sign-Changing Weight