Some multiplicity results of homoclinic solutions for second order Hamiltonian systems
Copyright policy )Some multiplicity results of homoclinic solutions for second order Hamiltonian systems
We look for homoclinic solutions \(q:\mathbb{R} \rightarrow \mathbb{R}^N\) to the class of second order Hamiltonian systems \[-\ddot{q} + L(t)q = a(t) \nabla G_1(q) - b(t) \nabla G_2(q) + f(t) \quad t \in \mathbb{R}\] where \(L: \mathbb{R}\rightarrow \mathbb{R}^{N \times N}\) and \(a,b: \mathbb{R}\rightarrow \mathbb{R}\) are positive bounded functions, \(G_1, G_2: \mathbb{R}^N \rightarrow \mathbb{R}\) are positive homogeneous functions and \(f:\mathbb{R}\rightarrow\mathbb{R}^N\). Using variational techniques and the Pohozaev fibering method, we prove the existence of infinitely many solutions if \(f\equiv 0\) and the existence of at least three solutions if \(f\) is not trivial but small enough.
second order hamiltonian systems, T57-57.97, Applied mathematics. Quantitative methods, homoclinic solutions, variational methods, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Homoclinic and heteroclinic solutions to ordinary differential equations, compact imbeddings, Variational principles in infinite-dimensional spaces, 510, compact embeddings, Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods, second-order Hamiltonian systems, Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems, Second order Hamiltonian systems
second order hamiltonian systems, T57-57.97, Applied mathematics. Quantitative methods, homoclinic solutions, variational methods, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Homoclinic and heteroclinic solutions to ordinary differential equations, compact imbeddings, Variational principles in infinite-dimensional spaces, 510, compact embeddings, Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods, second-order Hamiltonian systems, Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems, Second order Hamiltonian systems
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