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Some multiplicity results of homoclinic solutions for second order Hamiltonian systems

Barile Sara, Salvadore Addolorata

Opuscula Mathematica

2020

Vol. 40, no. 1

21--36

We look for homoclinic solutions [formula] to the class of second order Hamiltonian systems [formula] where [formula] and a, b : R → R are positive bounded functions, [formula] are positive homogeneous functions and [formula]. Using variational techniques and the Pohozaev fibering method, we prove the existence of infinitely many solutions if = 0 and the existence of at least three solutions if ƒ is not trivial but small enough.