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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board Member: Armstrong, Scott N. / Astala, Kari / Colding, Tobias / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Finster, Felix / Gianazza, Ugo / Gursky, Matthew / Hardt, Robert / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / McCann, Robert / Mingione, Giuseppe / Nystrom, Kaj / Pacard, Frank / Preiss, David / Riviére, Tristan / Schaetzle, Reiner / Silvestre, Luis

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1864-8266
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A note on the stability of solutions to quasilinear elliptic equations

Jagmohan Tyagi
  • Indian Institute of Technology Gandhinagar, Vishwakarma Government Engineering College Complex, Chandkheda, Visat-Gandhinagar Highway, Ahmedabad, Gujarat, India–382424
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Published Online: 2012-12-20 | DOI: https://doi.org/10.1515/acv-2012-0014

Abstract.

In this note, we prove a stability theorem for a class of quasilinear elliptic equations

where , , is an open, smooth and bounded subset. We show that if u is an unstable solution of the above problem, then u vanishes at some point of . In this work, a and f may change sign.

Keywords: p-Laplacian; stability; zeros

About the article

Received: 2012-07-07

Revised: 2012-10-28

Accepted: 2012-11-05

Published Online: 2012-12-20

Published in Print: 2013-10-01


Citation Information: Advances in Calculus of Variations, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2012-0014.

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