July/August 2015 Symmetry and multiple solutions for certain quasilinear elliptic equations
Roberta Filippucci, Patrizia Pucci, Csaba Varga
Adv. Differential Equations 20(7/8): 601-634 (July/August 2015). DOI: 10.57262/ade/1431115710


We present some symmetrization results which we apply to the same abstract eigenvalue problem in order to show the existence of three different solutions which are invariant by Schwarz symmetrization. In particular, we introduce two different methods in order to prove the existence of multiple symmetric solutions. The first is based on the symmetric version of the Ekeland variational principle and the mountain pass theorem, while the latter consists of an application of a suitable symmetric version of the three critical points theorem due to Pucci and Serrin [17, 18], see Theorem 2.13 and its Corollary 2.14. Using the second method, we are able to improve some recent results of Arcoya and Carmona [1] and Bonnano and Candito [2]. The methods we present work also for different types of symmetrization, see Van Schaftingen [22].


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Roberta Filippucci. Patrizia Pucci. Csaba Varga. "Symmetry and multiple solutions for certain quasilinear elliptic equations." Adv. Differential Equations 20 (7/8) 601 - 634, July/August 2015. https://doi.org/10.57262/ade/1431115710


Published: July/August 2015
First available in Project Euclid: 8 May 2015

zbMATH: 1326.35144
MathSciNet: MR3344612
Digital Object Identifier: 10.57262/ade/1431115710

Primary: 35A15 , 35J15 , 35J20 , 35J62

Rights: Copyright © 2015 Khayyam Publishing, Inc.


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Vol.20 • No. 7/8 • July/August 2015
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