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Abstract
We will be concerned with the existence of homoclinics for second order Hamiltonian systems in R^N (N>2) given by Hamiltonians of the form H(t,q,p)=Φ(p)+V(t,q), where Φ is a G-function in the sense of Trudinger, V is C^2-smooth, periodic in the time variable, has a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin. Under a strong force type condition aroud the singular point ξ, we prove the existence of a homoclinic solution, avoiding the singularity, via minimization of an action integral defined in an appropriate Orlicz-Sobolev space. We find a candidate for a solution as weak limit of a minimizing sequence and show directly that it is a critical point of the action functional. Our results extend those by Tanaka in [28].
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Authors (3)
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Nils Waterstraat dr
- Naturwissenschaftliche Fakultät II, Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
no. 60,
pages 1 - 18,
ISSN: 0944-2669 - Language:
- English
- Publication year:
- 2021
- Bibliographic description:
- Izydorek M., Janczewska J., Waterstraat N.: Homoclinics for singular strong force Lagrangian systems in R^N// CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS -Vol. 60,iss. 2 (2021), s.1-18
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s00526-021-01942-6
- Sources of funding:
- Verified by:
- Gdańsk University of Technology
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