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June, 2018 Existence and Multiplicity of Solutions for a Quasilinear Elliptic Inclusion with a Nonsmooth Potential
Ziqing Yuan, Lihong Huang, Dongshu Wang
Taiwanese J. Math. 22(3): 635-660 (June, 2018). DOI: 10.11650/tjm/170809


This paper is concerned with a nonlinear elliptic inclusion driven by a multivalued subdifferential of nonsmooth potential and a nonlinear inhomogeneous differential operator. We obtain two multiplicity theorems in the Orlicz-Sobolev space. In the first multiplicity theorem, we produce three nontrivial smooth solutions. Two of these solutions have constant sign (one is positive, the other is negative). In the second multiplicity theorem, we derive an unbounded sequence of critical points for the problem. Our approach is variational, based on the nonsmooth critical point theory. We also show that $C^1$-local minimizers are also local minimizers in the Orlicz-Sobolev space for a large class of locally Lipschitz functions.


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Ziqing Yuan. Lihong Huang. Dongshu Wang. "Existence and Multiplicity of Solutions for a Quasilinear Elliptic Inclusion with a Nonsmooth Potential." Taiwanese J. Math. 22 (3) 635 - 660, June, 2018.


Received: 23 December 2016; Revised: 16 May 2017; Accepted: 22 August 2017; Published: June, 2018
First available in Project Euclid: 4 October 2017

zbMATH: 06965390
MathSciNet: MR3807330
Digital Object Identifier: 10.11650/tjm/170809

Primary: 35J70 , 35R70 , 49J52

Keywords: locally Lipschitz , nonsmooth critical point , nonsmooth fountain theorem , Orlicz-Sobolev space , second deformation theorem

Rights: Copyright © 2018 The Mathematical Society of the Republic of China


Vol.22 • No. 3 • June, 2018
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