A continuous spectrum for nonhomogeneous differential operators in orlicz-sobolev spaces

19Citations
Citations of this article
6Readers
Mendeley users who have this article in their library.

Abstract

We study the nonlinear eigenvalue problem - div(a(Vu|)Vu) = λ|u|q(x)- 2 in Ω, u = 0 on ∂Ω, where Ω is a bounded open set in RN with smooth boundary, q is a continuous function, and a is a nonhomogeneous potential. We establish sufficient conditions on a and q such that the above nonhomogeneous quasilinear problem has continuous families of eigenvalues. The proofs rely on elementary variational arguments. The abstract results of this paper are illustrated by the cases a(t) = tp-2 log(1 + tr) and a(t) = tp-2[log(1 + t)|1.

Cite

CITATION STYLE

APA

Mihǎilescu, M., & Rǎdulescu, V. (2009). A continuous spectrum for nonhomogeneous differential operators in orlicz-sobolev spaces. Mathematica Scandinavica, 104(1), 132–146. https://doi.org/10.7146/math.scand.a-15090

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free