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Stability under Γ-convergence of least energy solutions for semilinear problems in the whole ℝN

Moameni, A ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1137/100810940
  3. Publisher: 2011
  4. Abstract:
  5. We study the homogenization of semilinear elliptic equations in divergence form with discontinuous oscillating coefficients in the whole ℝN. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions u Isin; of boundary value problems when the period ∈ > 0 of the coefficients is small. By extending some of the classical homogenization results for quasi-linear elliptic equations to unbounded domains and, making use of various variational techniques, we shall establish some stability results under Γ-convergence of least energy solutions for such boundary value problems
  6. Keywords:
  7. Schrödinger equations ; Asymptotic behavior of solutions ; Dinger equation ; Divergence form ; Homogenization ; Homogenization process ; Least energy solutions ; Quasilinear elliptic equations ; Semilinear ; Semilinear elliptic equation ; Stability results ; Unbounded domain ; Variational methods ; Boundary value problems ; Homogenization method ; Variational techniques ; Behavioral research
  8. Source: SIAM Journal on Mathematical Analysis ; Volume 43, Issue 4 , 2011 , Pages 1759-1786 ; 00361410 (ISSN)
  9. URL: http://epubs.siam.org/doi/abs/10.1137/100810940