TY  - JOUR
ID  - Barile2020
LB  - Barile2020
AU  - Barile, Sara
AU  - Salvatore, Addolorata
TI  - Some multiplicity results of homoclinic solutions for second order Hamiltonian systems
ST  - Some multiplicity results of homoclinic solutions for second order Hamiltonian systems
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 1
SP  - 21
EP  - 36
DO  - https://doi.org/10.7494/OpMath.2020.40.1.21
UR  - https://doi.org/10.7494/OpMath.2020.40.1.21
AB  - 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.
KW  - second order Hamiltonian systems
KW  - homoclinic solutions
KW  - variational methods
KW  - compact embeddings
SN  - 1232-9274
ER  -