Periodic Solutions of a Class of Second Order Functional Differential Equations

Zheng Qiu Zhang1, Zhi Cheng Wang1
1Department of Applied Mathematics, Hunan University, Changsha 410082, P. R. China

Tóm tắt

Từ khóa


Tài liệu tham khảo

Lazer, A. C.: On Schauder’s fixed point theorem and forced second–order nonlinear oscillations. J. Math. Anal. Appl., 21, 421–425 (1968)

Mawhin, J., Ward, J. R.: Periodic solutions of some forced Liénard differential equations at resonance. Arch. Math., 41, 337–351 (1983)

Caristi, G.: Monotone perturbations of linear operator having nullspace made of oscillating functions. Nonlinear Anal., 11(7), 851–860 (1987)

Mawhin, J., Willem, M.: Critical Point Theory and Hamiltonian System, Springer–Verlag, New York, Berlin, 1989

Mawhin, J.: Nonlinear oscillations: One hundred years after Liapunov and Poincare. Z. Angew. Math. Mech., 73 (4–5), T54–T62 (1993)

Gossez, J. P., Omari, P.: Periodic solutions of a second order ordinary differential equation: A necessary and sufficient condition for nonresonance. J. Differential Equations, 94, 67–82 (1991)

Ma, S. W., Wang, Z. C., Yu, J. S.: Coincidence degree and periodic solutions of Duffing equations. Nonlinear Analysis, 34, 443–460 (1998)

Huang, X. K., Xing, Z. G.: 2π–periodic solution of Duffing equation with a deviating argument. Chinese, Sci. Bull. (Chinese), 39(3), 201–203 (1994)

Iannacci, R., Nkashama, M. N.: Unbounded perturbations of forced second order ordinary differential equations at resonance. J. Differential Equations, 69, 298–309 (1987)

Manasevich, R., Mawhin, J.: Periodic solutions for nonlinear systems with P–Laplacian–Like operators. J. Differential Equations, 145, 367–393 (1998)

Zhang, M.: Periodic solutions of Liénard equation with singular forces of repulsive type. J. Math. Anal. Appl., 203, 254–269 (1996)

Nguyen Phuony Cae: Periodic solutions of a second order nonlinear system. J. Math. Anal. Appl., 214, 219–232 (1997)

Katriel, G.: Many periodic solutions for pendulum–type equations. Nonlinear Analysis, 34, 687–699 (1998)

Omari, P.: Periodic solutions of the Liénard equation with one–sided growth restrictions. J. Differential Equations, 67, 278–293 (1987)

Mawhin, J.: Periodic solutions of nonlinear functional differential equations. J. Differential Equations, 10, 240–261 (1971)

Manasevich, R., Mawhin, J., Zanolin, F.: Periodic solutions of some complex–valued Lienard and Rayleigh equations. Nonlinear Analysis, 36, 997–1014 (1999)

Heiden, U. An Der: Periodic solutions of a nonlinear second order differential equation with delay. J. Math. Anal. Appl., 70, 579–609 (1979)

Gaines, R. E., Mawhin, J. L.: Coincidence Degree, and Non–linear Differential Equation, Springer–Verlag, Berlin, 1977