New Homoclinic Orbits for Hamiltonian Systems with Asymptotically Quadratic Growth at Infinity

Dong-Lun Wu; Xiang Yu

Ayuda

New Homoclinic Orbits for Hamiltonian Systems with Asymptotically Quadratic Growth at Infinity

Dong-Lun, Wu ^[1] ; Yu, Xiang ^[2]
1. [1] Southwest Petroleum University
  
  Southwest Petroleum University
  
  China
2. [2] Southwestern University of Finance and Economics
  
  Southwestern University of Finance and Economics
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
Idioma: inglés
DOI: 10.1007/s12346-020-00346-9
Enlaces
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Resumen
- In this paper, we study the existence and multiplicity of homoclinic solutions for following Hamiltonian systems with asymptotically quadratic nonlinearities at infinity u¨(t)-L(t)u+∇W(t,u)=0.We introduce a new coercive condition and obtain a new embedding theorem. With this theorem, we show that above systems possess at least one nontrivial homoclinic orbits by generalized mountain pass theorem. By variant fountain theorem, infinitely many homoclinic orbits are obtained for above problem with symmetric condition. Our asymptotically quadratic conditions are different from previous ones in the references.
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