Abstract
<abstract><p>The paper is devoted to obtain new results of positive doubly periodic solutions to telegraph equations. One of the interesting features in our proof is that we give a new attempt to solve telegraph equation by using the theory of Hilbert's metric. Then we apply the eigenvalue theory to analyze the existence, multiplicity, nonexistence and asymptotic behavior of positive doubly periodic solutions. We also study a corresponding eigenvalue problem in a more general case.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference27 articles.
1. V. Barbu, Nonlinear boundary value problems for a class of hyperbolic systems, Rev. Roum. Math. Pures Appl., 22 (1977), 155–168.
2. G. Roussy, J. A. Pearcy, Foundations and Industrial Applications of Microwaves and Radio Frequency Fields, Wiley, New York, 1995.
3. Y. Li, Maximum principles and the method of upper and lower solutions for time-periodic problems of the telegraph equations, J. Math. Anal. Appl., 327 (2007), 997–1009. https://doi.org/10.1016/j.jmaa.2006.04.066
4. J. Mawhin, R. Ortega, A. M. Robles-Pérez, Maximum principles for bounded solutions of the telegraph equation in space dimensions two and three and applications, J. Differ. Equ., 208 (2005), 42–63. https://doi.org/10.1016/j.jde.2003.11.003
5. J. Mawhin, R. Ortega, A. M. Robles-Pérez, A maximum principle for bounded solutions of the telegraph equation in space dimension three, C. R. Acad. Sci. Paris, Ser. I, 334 (2002), 1089–1094. https://doi.org/10.1016/S1631-073X(02)02406-8
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