The $$\infty $$ ∞ -eigenvalue problem with a sign-changing weight
نویسندگان
چکیده
منابع مشابه
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 ...
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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.
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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...
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ژورنال
عنوان ژورنال: Nonlinear Differential Equations and Applications NoDEA
سال: 2019
ISSN: 1021-9722,1420-9004
DOI: 10.1007/s00030-019-0561-y