Dimova, MilenaKolkovska, NataliaKutev, Nikolai2022-01-262022-01-262018-03-14Dimova, M., Kolkovska, N., & Kutev, N. (2018). Blow up of solutions to ordinary differential equations arising in nonlinear dispersive problems. <i>Electronic Journal of Differential Equations, 2018</i>(68), pp. 1-16.1072-6691https://hdl.handle.net/10877/15210We study a new class of ordinary differential equations with blow up solutions. Necessary and sufficient conditions for finite blow up time are proved. Based on the new differential equation, a revised version of the concavity method of Levine is proposed. As an application we investigate the non-existence of global solutions to the Cauchy problem of Klein-Gordon, and to the double dispersive equations. We obtain necessary and sufficient condition for finite time blow up with arbitrary positive energy. A very general sufficient condition for blow up is also given.Text16 pages1 file (.pdf)enAttribution 4.0 InternationalFinite time blow upConcavity methodKlein-Gordon equationDouble dispersive equationArticle