Positive doubly periodic solutions of nonlinear telegraph equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 55, Issue 3, 2003, Pages 245-254

  Li, Yongxiang ^a,b  

^a NORTHWEST NORMAL UNIVERSITY   (China)

^b LANZHOU UNIVERSITY   (China)

Author keywords

Cone; Doubly periodic solution; Fixed point theorem of cone mapping; Telegraph equation

Indexed keywords

BOUNDARY VALUE PROBLEMS; FUNCTIONS; THEOREM PROVING;

PERIODIC SOLUTIONS;

NONLINEAR EQUATIONS;

EID: 0041387383     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(03)00227-X     Document Type: Article

References (12)

1. Birnir B., Grauer R. An explicit description of the global attractor of the damped and driven sine-Gordon equation. Comm. Math. Phys. 162:1994;539-590.
2. W. Eloe P., Henderson J. Positive solutions for. (n-1,1) conjugate boundary value problems Nonlinear Anal. 28:1997;1669-1680.
3. Erbe L.H., Wang H. On the existence of the positive solutions of ordinary differential equations. Proc. Amer. Math. Soc. 120:1994;743-748.
4. Fucik S., Mawhin J. Generated periodic solution of nonlinear telegraph equation. Nonlinear Anal. 2:1978;609-617.
5. Guo D., Lakshmikantham V. Nonlinear Problems in Abstract Cones. 1988;Academic Press, New York.
6. Kim W.S. Double-periodic boundary value problem for nonlinear dissipative hyperbolic equations. J. Math. Anal. Appl. 145:1990;1-16.
7. Kim W.S. Multiple doubly periodic solutions of semilinear dissipative hyperbolic equations. J. Math. Anal. Appl. 197:1996;735-748.
8. J. Mawhin, Periodic solution of nonlinear telegraph equations, in: A.R. Bedlarek, L. Cesari (Eds.), Dynamical Systems, Academic Press, New York, 1977.
9. Ortega R., Robles-Perez A.M. A maximum principle for periodic solutions of the telegraph equations. J. Math. Anal. Appl. 221:1998;625-651.
10. Ortega R., Robles-Perez A.M. A duality theorem for periodic solutions of a class of second order evolution equations. J. Differential Equations. 172:2001;409-444.
11. Vejvoda O. Partial Differential Equations: Time-Periodic Solutions. 1982;Nijhoff, Prague.
12. Yongxiang Li, Positive periodic solutions of nonlinear second-order ordinary differential equations, Acta Math. Sinica, 45 (2002) 481-488, (in Chinese).