Continuous Spectrum of a Fourth Order Nonhomogeneous Elliptic Equation with Variable Exponent

@inproceedings{Amrouss2011ContinuousSO,
  title={Continuous Spectrum of a Fourth Order Nonhomogeneous Elliptic Equation with Variable Exponent},
  author={A. R. El Amrouss},
  year={2011}
}
In this article, we consider the nonlinear eigenvalue problem ∆(|∆u|p(x)−2∆u) = λ|u|q(x)−2u in Ω, u = ∆u = 0 on ∂Ω, where Ω is a bounded domain in RN with smooth boundary and p, q : Ω → (1, +∞) are continuous functions. Considering different situations concerning the growth rates involved in the above quoted problem, we prove the existence of a continuous family of eigenvalues. The proofs of the main results are based on the mountain pass lemma and Ekelands variational principle. 

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