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Strict Monotonicity and Unique Continuation for the Third‐Order Spectrum of Biharmonic Operator

Author

Listed:
  • Khalil Ben Haddouch
  • Zakaria El Allali
  • El Bekkaye Mermri
  • Najib Tsouli

Abstract

We will study the spectrum for the biharmonic operator involving the laplacian and the gradient of the laplacian with weight, which we call third‐order spectrum. We will show that the strict monotonicity of the eigenvalues of the operator Δ2u + 2β · ∇(Δu)+|β|2Δu, where β ∈ ℝN, holds if some unique continuation property is satisfied by the corresponding eigenfunctions.

Suggested Citation

  • Khalil Ben Haddouch & Zakaria El Allali & El Bekkaye Mermri & Najib Tsouli, 2012. "Strict Monotonicity and Unique Continuation for the Third‐Order Spectrum of Biharmonic Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:571951
    DOI: 10.1155/2012/571951
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    References listed on IDEAS

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    1. D. G. De Figueiredo & P. L. Lions & R. D. Nussbaum, 1982. "A Priori Estimates and Existence of Positive Solutions of Semilinear Elliptic Equations," Springer Books, in: David G. Costa (ed.), Djairo G. de Figueiredo - Selected Papers, edition 127, pages 133-155, Springer.
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