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A limiting problem for a family of eigenvalue problems involving p-Laplacians

  • Mihai Mihăilescu
  • Julio D. RossiEmail author
  • Denisa Stancu-Dumitru
Article
  • 13 Downloads

Abstract

In this paper we analyse the existence of principal eigenvalues and eigenfunctions for a family of eigenvalue problems described by a system consisting in two partial differential equations involving p-Laplacians. Next, we study the asymptotic behaviour, as \(p\rightarrow \infty \), of the sequence of principal eigenfunctions and we show that, passing eventually to a subsequence, it converges uniformly to a certain limit given by a pair of continuous functions. Moreover, we identify the limiting equations which have as solutions the limiting functions.

Keywords

Eigenvalue problem Weak solution Distance function \(\Gamma \)-convergence Viscosity solution 

Mathematics Subject Classification

35D30 35D40 46E30 46E35 49J40 49J45 

Notes

Acknowledgements

The research of MM and DSD was partially supported by CNCS-UEFISCDI Grant No. PN-III-P4-ID-PCE-2016-0035 while JDR was partially supported by CONICET Grant PIP GI No 11220150100036CO (Argentina), by UBACyT Grant 20020160100155BA (Argentina) and by MINECO MTM2015-70227-P (Spain).

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Copyright information

© Universidad Complutense de Madrid 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CraiovaCraiovaRomania
  2. 2.Research group of the project PN-III-P4-ID-PCE-2016-0035“Simion Stoilow” Institute of Mathematics of the Romanian AcademyBucharestRomania
  3. 3.Dep. de MatemáticaFCEyN, Universidad de Buenos AiresBuenos AiresArgentina
  4. 4.Department of Mathematics and Computer SciencesUniversity Politehnica of BucharestBucharestRomania

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