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Abstract
Abstract. This paper is concerned with the following Euler-Lagrange system d/dtLv(t,u(t), ̇u(t)) =Lx(t,u(t), ̇u(t)) for a.e.t∈[−T,T], u(−T) =u(T), Lv(−T,u(−T), ̇u(−T)) =Lv(T,u(T), ̇u(T)), where Lagrangian is given by L=F(t,x,v) +V(t,x) +〈f(t),x〉, growth conditions aredetermined by an anisotropic G-function and some geometric conditions at infinity.We consider two cases: with and without forcing termf. Using a general version ofthe mountain pass theorem and Ekeland’s variational principle we prove the existenceof at least two nontrivial periodic solutions in an anisotropic Orlicz-Sobolev space.
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- Copyright (2021 The Mathematical Society of the Republic of China)
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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TAIWANESE JOURNAL OF MATHEMATICS
no. 25,
pages 409 - 425,
ISSN: 1027-5487 - Language:
- English
- Publication year:
- 2021
- Bibliographic description:
- Chmara M.: Existence of Two Periodic Solutions to General Anisotropic Euler-Lagrange Equations// TAIWANESE JOURNAL OF MATHEMATICS -Vol. 25,iss. 2 (2021), s.409-425
- DOI:
- Digital Object Identifier (open in new tab) 10.11650/tjm/200902
- Verified by:
- Gdańsk University of Technology
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