Bereanu, Cristian An Ambrosetti-Prodi-type result for periodic solutions of the telegraph equation. (English) Zbl 1149.35059 Proc. R. Soc. Edinb., Sect. A, Math. 138, No. 4, 719-724 (2008). Summary: Using Leray-Schauder degree theory, a theorem of upper and lower solutions and a strong maximum principle for the telegraph equation \[ \begin{aligned} &u_{tt}-u_{xx}+ cu_t+f(t,x,u)=s,\\ &u(t+2\pi,x)= u(t,x+2\pi)= u(t,x), \quad (t,x)\in\mathbb R^2, \end{aligned} \]where \(c>0\), \(f:\mathbb R^3\to\mathbb R\) is a continuous function \(2\pi\)-periodic in \(t\) and \(x\), \(s\) is a real parameter. We prove an Ambrosetti-Prodi-type result for periodic solutions of the telegraph equation. Cited in 7 Documents MSC: 35L70 Second-order nonlinear hyperbolic equations 35B10 Periodic solutions to PDEs 35B50 Maximum principles in context of PDEs Keywords:Leray-Schauder degree theory; upper and lower solutions PDFBibTeX XMLCite \textit{C. Bereanu}, Proc. R. Soc. Edinb., Sect. A, Math. 138, No. 4, 719--724 (2008; Zbl 1149.35059) Full Text: DOI