On the global center of generalized Liénard equation and its application to stability problems

1 Burton, T. A. On the equation $x''+f(x)h(x')x'+g(x)=e(t)$ Ann. Mat. Pura Appl. 85 1970 277-285 MR0262595 Cache/Bu/Burton,x''+f(x)h(x')x'+g(x)=e(t),Ann*,1970,1971

2 Burton, T. A.; Townsend, C. G. On the generalized Liénard equation with forcing function J. Differential Equations 4 1968 620-633 MR0232042 100 Cache/Bu/Burton,generalized,J*,1968,1969

3 De Figueiredo, R. J. P. On the existence of n periodic solutions of Lénard's equation Nonlinear Analysis 7 1983 483-499 MR0698361 90 Cache/De/De Figueiredo,existence,Nonlinear*,1983,1984

4 Filippov, A. F. Sufficient conditions for the existence of stable limit cycles of second order equations Mat. Sb. 30(72) 1952 171-180 MR0047869 94 Cache/Fi/Filippov,Sufficient,Mat*,1952,1953

5 Graef, J. R. On the generalized Liénard equation with negative damping J. Differential Equations 12 1972 34-62 MR0328200 100 Cache/Gr/Graef,generalized,J*,1972,1973

6 Graef, J. R.; Spikes, P. W. Boundedness and convergence to zero of solutions of a forced second order nonlinear differential equation J. Math. Anal. Appl. 62 1978 295-309 MR0492527 92 Cache/Gr/Graef,Boundedness,J*,1978,1979

7 Graef, J. R.; Spikes, P. W. Asymptotic behavior of solutions of a second order linear differential equations J. Differential Equations 17 1975 461-476 MR0361275 90 Cache/Gr/Graef,Asymptotic,J*,1975,1976

8 Hara, T.; Yoneyama, T.; Sugie, J. Continuation results for differential equations by two Liapunov functions Ann. Mat. Pura Appl. 133 1983 79-92 MR0725020 100 Cache/Ha/Hara,Continuation,Ann*,1983,1984

9 Hara, T.; Yoneyama, T.; Sugie, J., Necessary and sufficient conditions for the continuability of solutions of the system $x'=y-F(x)$, $y'=-g(x)$, to be published in Applicable Analysis MR0800167

10 Heidel, J. W. A Liapunov function for a generalized Liénard equation J. Math. Anal. Appl. 39 1972 192-197 MR0322283 100 Cache/He/Heidel,generalized,J*,1972,1973

11 McHarg, E. A differential equation J. London Math. Soc. 22 1947 83-85 MR0023992 100 Cache/Mc/McHarg,A,J*,1947,1948

12 Opial, Z. Sur un théorème de A. Filippoff Ann. Polon. Math. 5 1958 67-75 MR0097584 100 Cache/Op/Opial,Sur,Ann*,1958,1959

13 Ponzo, P. J.; Wax, N. On periodic solutions of the system $\dot{x}=y-F(x)$, $\dot{y}=-g(x)$ J. Differential Equations 10 1971 262-269 MR0288360 100 Cache/Po/Ponzo,solutions,J*,1971,1972

14 Reissig, R.; Sansone, G.; Conti, R. Qualitative Theorie Nichtlinearer Differentialgleichungen Cremonese, Rome 1963 MR0158121 100 Cache/Re/Reissig,Differentialgleichungen,*,1963,1964 xxxii+381

15 Sandqvist, A.; Andersen, K. Munk. A necessary and sufficient condition for the existence of a unique nontrivial periodic solution to a class of equations of Liénard's type J. Differential Equations 46 1982 356-378 MR0681229 100 Cache/Sa/Sandqvist,sufficient,J*,1982,1983

16 Sansone, G.; Conti, R. Non-linear Differential Equations Macmillan, New York 1964 MR0177153 100 Cache/Sa/Sansone,Non-linear,*,1964,1965 xiii+536

17 Staude, U. Uniqueness of periodic solutions of the Liénard equation Recent Advance in Differential Equations, Academic Press, New York 1981 421-429 MR0643151 Cache/St/Staude,Uniqueness,*,1981,1982

18 Villari, G. On the existence of periodic solutions for Lénard's equation Nonlinear Analysis 7 1983 71-78 MR0687031 88 Cache/Vi/Villari,existence,Nonlinear*,1983,1984

19 Villari, G. Periodic solutions of Liénard's equation J. Math. Anal. Appl. 86 1982 379-386 MR0652183 100 Cache/Vi/Villari,solutions,J*,1982,1983

20 Wendel, J. G. On a van der Pol equation with odd coefficients J. London Math. Soc. 24 1949 65-67 MR0029034 100 Cache/We/Wendel,coefficients,J*,1949,1950

21 Yamamoto, M.; Sakata, S. On the boundedness of solutions and the attractivity properties for nonlinear second-order differential equations Math. Japon. 27 1982 231-251 MR0655227 100 Cache/Ya/Yamamoto,attractivity,Math*,1982,1983

22 Yoshizawa, T. Stability theory by Liapunov's second method Math. Soc. Japan, Tokyo 1966 MR0208086 100 Cache/Yo/Yoshizawa,Liapunov's,*,1966,1967 viii+223