Wang, Fanglei Doubly periodic solutions of a coupled nonlinear telegraph system with weak singularities. (English) Zbl 1202.35018 Nonlinear Anal., Real World Appl. 12, No. 1, 254-261 (2011). Summary: A weak force condition enables the achievement of new existence criteria for positive doubly periodic solutions of a nonlinear telegraph system through a basic application of Schauder’s fixed point theorem. A weak singularity will be useful to our proofs. Cited in 4 Documents MSC: 35B10 Periodic solutions to PDEs 35L53 Initial-boundary value problems for second-order hyperbolic systems 35L71 Second-order semilinear hyperbolic equations Keywords:Schauder’s fixed point theorem; new existence criteria PDFBibTeX XMLCite \textit{F. Wang}, Nonlinear Anal., Real World Appl. 12, No. 1, 254--261 (2011; Zbl 1202.35018) Full Text: DOI References: [1] Chu, J.; Torres, P. J.; Zhang, M., Periodic solutions of second order non-autonomous singular dynamical systems, J. Differential Equations, 239, 196-212 (2007) · Zbl 1127.34023 [2] Torres, P. J., Weak singularities may help periodic solutions to exist, J. Differential Equations, 232, 277-284 (2007) · Zbl 1116.34036 [3] Kim, W. S., Doubly-periodic boundary value problem for nonlinear dissipative hyperbolic equations, J. Math. Anal. Appl., 145, 1-6 (1990) [4] Kim, W. S., Multiple doubly periodic solutions of semilinear dissipative hyperbolic equations, J. Math. Anal. Appl., 197, 735-748 (1996) · Zbl 0870.35069 [5] Li, Y., Positive doubly periodic solutions of nonlinear telegraph equations, Nonlinear Anal., 55, 245-254 (2003) · Zbl 1036.35020 [6] Li, Y., Maximum principles and method of upper and lower solutions for time-periodic problems of the telegraph equations, J. Math. Anal. Appl., 327, 997-1009 (2007) · Zbl 1108.35021 [7] Mawhin, J., Periodic solution of nonlinear telegraph equations, (Bedlarek, A. R.; Cesari, L., Dynamical Systems (1977), Academic Press: Academic Press New York) · Zbl 1098.35022 [8] Mawhin, J.; Ortega, R.; Robles-Perez, A. M., A maximum principle for bounded solutions of the telegraph equations and applications to nonlinear forcings, J. Math. Anal. Appl., 251, 695-709 (2000) · Zbl 0972.35016 [9] Mawhin, J.; Ortega, R.; Robles-Perez, A. M., Maximum principles for bounded solutions of the telegraph equation in space dimensions two or three and applications, J. Differential Equations, 208, 42-63 (2005) · Zbl 1082.35040 [10] Ortega, R.; Robles-Perez, A. M., A maximum principle for periodic solutions of the telegraph equations, J. Math. Anal. Appl., 221, 625-651 (1998) · Zbl 0932.35016 [11] Wang, F.; An, Y., Nonnegative doubly periodic solutions for nonlinear telegraph system, J. Math. Anal. Appl., 338, 91-100 (2008) · Zbl 1145.35010 [12] Wang, F.; An, Y., Existence and multiplicity results of positive doubly periodic solutions for nonlinear telegraph system, J. Math. Anal. Appl., 349, 30-42 (2009) · Zbl 1159.35011 [13] Wang, F.; An, Y., A generalized quasilinearization method for telegraph system, Nonlinear Anal. RWA, 11, 407-413 (2010) · Zbl 1180.35146 [14] Guo, D.; Lakshmikantham, V., Nonlinear Problems in Abstract Cones (1988), Academic Press: Academic Press New York · Zbl 0661.47045 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.