Bereanu, Cristian Periodic solutions of the nonlinear telegraph equations with bounded nonlinearities. (English) Zbl 1144.35005 J. Math. Anal. Appl. 343, No. 2, 758-762 (2008). Summary: In this article, using the Leray-Schauder degree theory, we discuss existence, nonexistence and multiplicity for the periodic solutions of the nonlinear telegraph equation \[ u_{tt}- u_{xx}+ cu_t+ \Phi(u)= f(t, x)+ s, \] where \(c> \)0, \(\Phi\in C(\mathbb{R})\), \(f\in C(\mathbb{T}^2)\) and \(s\) is a parameter. Cited in 13 Documents MSC: 35B10 Periodic solutions to PDEs 35L70 Second-order nonlinear hyperbolic equations 35L20 Initial-boundary value problems for second-order hyperbolic equations Keywords:Leray-Schauder degree; periodicity in space and time; existence; nonexistence; multiplicity PDFBibTeX XMLCite \textit{C. Bereanu}, J. Math. Anal. Appl. 343, No. 2, 758--762 (2008; Zbl 1144.35005) Full Text: DOI References: [1] Amann, H.; Ambrosetti, A.; Mancini, G., Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities, Math. Z., 158, 179-194 (1978) · Zbl 0368.35032 [2] C. Bereanu, J. Mawhin, Multiple periodic solutions of ordinary differential equations with bounded nonlinearities and Φ;-Laplacian, NoDEA Nonlinear Differential Equations Appl., in press; C. Bereanu, J. Mawhin, Multiple periodic solutions of ordinary differential equations with bounded nonlinearities and Φ;-Laplacian, NoDEA Nonlinear Differential Equations Appl., in press · Zbl 1146.34035 [3] De Coster, C.; Tarallo, M., Foliations, associated reductions and lower and upper solutions, Calc. Var., 15, 25-44 (2002) · Zbl 1026.34018 [4] Cid, J.Á.; Sanchez, L., Periodic solutions for second order differential equations with discontinuous restoring forces, J. Math. Anal. Appl., 288, 349-364 (2003) · Zbl 1054.34012 [5] Fucik, S.; Mawhin, J., Generalized periodic solutions of nonlinear telegraph equations, Nonlinear Anal., 2, 609-617 (1978) · Zbl 0381.35056 [6] Ortega, R.; Robles-Pérez, A. M., A maximum principle for periodic solutions of the telegraph equation, J. Math. Anal. Appl., 221, 625-651 (1998) · Zbl 0932.35016 [7] Ortega, R.; Robles-Pérez, A. M., A duality theorem for periodic solutions of a class of second order evolution equations, J. Differential Equations, 172, 409-444 (2001) · Zbl 1010.34054 [8] Ward, J. R., Periodic solutions of ordinary differential equations with bounded nonlinearities, Topol. Methods Nonlinear Anal., 19, 275-282 (2002) · Zbl 1016.34011 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.