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March  2015, 14(2): 677-693. doi: 10.3934/cpaa.2015.14.677

## Refined blow-up results for nonlinear fourth order differential equations

 1 Dipartimento di Matematica Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano 2 School of Mathematics, Trinity College, Dublin 2

Received  May 2014 Revised  October 2014 Published  December 2014

We study a class of nonlinear fourth order differential equations which arise as models of suspension bridges. When it comes to power-like nonlinearities, it is known that solutions may blow up in finite time, if the initial data satisfy some positivity assumption. We extend this result to more general nonlinearities allowing exponential growth and to a wider class of initial data. We also give some hints on how to prevent blow-up.
Citation: Filippo Gazzola, Paschalis Karageorgis. Refined blow-up results for nonlinear fourth order differential equations. Communications on Pure & Applied Analysis, 2015, 14 (2) : 677-693. doi: 10.3934/cpaa.2015.14.677
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