Eigenvalues of p(x)-Laplacian Dirichlet problem

By Xianling Fan, Qihu Zhang, Dun Zhao. 2005

455 citations recorded by the source corpus.

Abstract This paper studies the eigenvalues of the p(x)-Laplacian Dirichlet problem − div (|∇u| p(x)−2 ∇u)=λ|u| p(x)−2 u in Ω, u=0 on ∂Ω, where Ω is a bounded domain in RN and p(x) is a continuous function on Ω such that p(x)>1. We show that Λ, the set of eigenvalues, is a nonempty infinite set such that supΛ=+∞. We present some sufficient conditions for infΛ=0 and for infΛ>0, respectively.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/78c605c04e62310de4a45aa2c4d80711381d6fca

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Quasilinear elliptic non-homogeneous Dirichlet problems through Orlicz-Sobolev spaces (2012, unknown): “[20–22,9,23].”
On the existence of stationary solutions for higher-order p-Kirchhoff problems (2014, background): “1 of [26] has been extended to the p(x)–biharmonic operator under Navier boundary conditions.”
On a nonhomogeneous quasilinear eigenvalue problem in sobolev spaces with variable exponent (2006, methodology): “The case p(x) = q(x) was considered by Fan, Zhang and Zhao in [14] who, using the Ljusternik-Schnirelmann critical point theory, established the existence of a sequence of eigenvalues.”
Overview of differential equations with non-standard growth (2010, unknown): “2, [96]).”
Global Nonexistence for Nonlinear Kirchhoff Systems (2010, unknown): “Last but not least, we recall that the nonhomogeneous p(x)-Kirchhoff operator has been used in the last decades tomodel various phenomena, see [9–16,19,26,27] and the references therein.”
A strong maximum principle for differential equations with nonstandard p(x)-growth conditions (2005, background): “There are already some results about this kind of problems (see [1–13,15–20,22,24,25]).”