Subharmonic and homoclinic solutions for second order Hamiltonian systems with new superquadratic conditions

Ground state homoclinic solutions for a second-order Hamiltonian system

“…In recent decades, the existence and multiplicity of homoclinic orbits for secondorder Hamiltonian systems and their discrete analogues have been widely investigated by many authors, see for example [1][2][3][5][6][7][8][9]12,[14][15][16][17][19][20][21][26][27][28][29][30][32][33][34][35][36][37][38][39][40] and the references therein. For the case when the condition (L1) L(t) is positive definite uniformly in t ∈ R is satisfied and 0 is a local minimum of the energy functional associated with (1.1), the Mountain-pass theorem proved itself as an effective tool to establish the existence and multiplicity of homoclinic solutions for (1.1), see for example 2164 XIAOPING WANG [5, 6, 14-17, 20, 21, 30, 34, 36].…”