Maximum principles and the method of upper and lower solutions for time-periodic problems of the telegraph equations

Journal of Mathematical Analysis and Applications

Volumn 327, Issue 2, 2007, Pages 997-1009

  Li, Yongxiang ^a  

^a NORTHWEST NORMAL UNIVERSITY   (China)

Author keywords

Maximum principle; Telegraph equation; Time periodic solution; Upper and lower solutions

Indexed keywords

EID: 33750988190     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.04.066     Document Type: Article

References (16)

1. Mawhin J. Periodic solution of nonlinear telegraph equations. In: Bedlarek A.R., and Cesari L. (Eds). Dynamical Systems (1977), Academic Press, New York
2. Fucik S., and Mawhin J. Generated periodic solution of nonlinear telegraph equation. Nonlinear Anal. 2 (1978) 609-617
3. Vejvoda O. Partial Differential Equations: Time-Periodic Solutions (1982), Martinus Nijhoff Publishers, Boston
4. Kim W.S. Boundary value problem for nonlinear telegraph equations with superlinear growth. Nonlinear Anal. 12 (1988) 1371-1376
5. Kim W.S. Double-periodic boundary value problem for nonlinear dissipative hyperbolic equations. J. Math. Anal. Appl. 145 (1990) 1-16
6. Kim W.S. Multiple doubly periodic solutions of semilinear dissipative hyperbolic equations. J. Math. Anal. Appl. 197 (1996) 735-748
7. Hirano N., and Kim W.S. Periodic-Dirichlet boundary value problem for semilinear dissipative hyperbolic equations. J. Math. Anal. Appl. 148 (1990) 371-377
8. Arias M. Nonselfadjoint boundary value problems at resonance with nonlinearities which may grow linearly. Nonlinear Anal. 15 (1990) 155-163
9. Birnir B., and Grauer R. An explicit description of the global attractor of the damped and driven sine-Gordon equation. Comm. Math. Phys. 162 (1994) 539-590
10. Ortega R., and Robles-Pérez A.M. A maximum principle for periodic solutions of the telegraph equations. J. Math. Anal. Appl. 221 (1998) 625-651
11. Ortega R., and Robles-Pérez A.M. A duality theorem for periodic solutions of a class of second order evolution equations. J. Differential Equations 172 (2001) 409-444
12. Grossinho M.R., and Nkashama M.N. Periodic solutions of parabolic and telegraph equations with asymmetric nonlinearities. Nonlinear Anal. 33 (1998) 187-210
13. Li Y. Positive doubly periodic solutions of nonlinear telegraph equations. Nonlinear Anal. 55 (2003) 245-254
14. Nieto J.J. An abstract monotone iterative technique. Nonlinear Anal. 28 (1997) 1923-1933
15. Mawhin J., Ortega R., and Robles-Pérez A.M. A maximum principle for bounded solutions of the telegraph equations and applications to nonlinear forcings. J. Math. Anal. Appl. 251 (2000) 695-709
16. Mawhin J., Ortega R., and Robles-Pérez A.M. Maximum principles for bounded solutions of the telegraph equation in space dimensions two or three and applications. J. Differential Equations 208 (2005) 42-63