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1. Homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign nonlinearities

Author

Dong-Lun Wu

Subjects
multiple homoclinic solutions, asymptotically autonomous hamiltonian systems, indefinite sign nonlinearities, best constant for sobolev inequality, the concentration-compactness principle, Mathematics, QA1-939
Abstract

In this paper, we obtain the multiplicity of homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign potentials. The concentration-compactness principle is applied to show the compactness. As a byproduct, we obtain the uniqueness of the positive ground state solution for a class of autonomous Hamiltonian systems and the best constant for Sobolev inequality which are of independent interests.

Published
2023
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