论文信息 - Multiple periodic solutions of the second order Hamiltonian systems with superlinear terms

Multiple periodic solutions of the second order Hamiltonian systems with superlinear terms

Abstract We study the existence of 2π-periodic solutions of the second order Hamiltonian systems − x ¨ − A ( t ) x = λ x + V x ′ ( t , x ) with superlinear terms and with saddle structure near the origin. Some multiplicity results are obtained by using bifurcation method, homological linking and Morse theory.

[1] Shu Jie Li. Periodic solutions of nonautonomous second order systems with superlinear terms , 1992, Differential and Integral Equations.

[2] Existence of multiple critical points for an asymptotically quadratic functional with applications , 1996 .

[3] Thomas Bartsch,et al. Critical point theory for asymptotically quadratic functionals and applications to problems with resonance , 1997 .

[4] Jiabao Su,et al. Multiple periodic solutions of ordinary differential equations with double resonance , 2009 .

[5] Wolfgang Meyer,et al. On differentiable functions with isolated critical points , 1969 .

[6] P. Rabinowitz. Some Critical Point Theorems and Applications to Semilinear Elliptic Partial Differential Equations. , 1978 .

[7] J. Mawhin,et al. Critical Point Theory and Hamiltonian Systems , 1989 .

[8] Jiabao Su,et al. Multiplicity results for asymptotically linear elliptic problems at resonance , 2003 .

[9] Paul H. Rabinowitz,et al. Periodic solutions of hamiltonian systems , 1978 .

[10] Zhi-Qiang Wang. On a superlinear elliptic equation , 1991 .

[11] P. Rabinowitz,et al. Multiple solutions of superlinear elliptic equations , 2007 .

[12] P. Rabinowitz. Minimax methods in critical point theory with applications to differential equations , 1986 .

[13] Kuang-Chao Chang. In nite Dimensional Morse Theory and Multiple Solution Problems , 1992 .