Yagdjian, Karen The semilinear Klein-Gordon equation in de Sitter spacetime. (English) Zbl 1194.35271 Discrete Contin. Dyn. Syst., Ser. S 2, No. 3, 679-696 (2009). The author investigates the blow-up phenomena for the solutions of the semilinear Klein-Gordon equation \(\square_g\phi-m^2 \phi = -|\phi |^p \) with the small mass \(m \leq n/2\) in de Sitter spacetime with the metric \(g\). The article rigorously demonstrates that for every \(p>1\) large energy solutions blow up, on the other hand it gives a borderline \(p=p(m,n)\) for the global in time existence, associated with the small energy solutions. The obsevations are based on the representation formulas for the solution of the Cauchy problem and on some generalizations of Kato’s lemma. Reviewer: Ömer Kavaklioglu (Izmir) Cited in 33 Documents MSC: 35L71 Second-order semilinear hyperbolic equations 35Q40 PDEs in connection with quantum mechanics 35Q75 PDEs in connection with relativity and gravitational theory 35B44 Blow-up in context of PDEs 35L15 Initial value problems for second-order hyperbolic equations Keywords:Kato’s lemma PDFBibTeX XMLCite \textit{K. Yagdjian}, Discrete Contin. Dyn. Syst., Ser. S 2, No. 3, 679--696 (2009; Zbl 1194.35271) Full Text: DOI arXiv