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"Concerning (partial) differential equations, amongst many others two questions are of great importance: existence and uniqueness, or more general multiplicity of solutions... There are plenty of equations, where analytical methods fail to work." The author describes in this work a computer-assisted method for proving existence and multiplicity of solutions of fourth order nonlinear elliptic boundary value problems. The main idea of this method is to compute a good numerical approximation of a solution and certain defect bounds with computer-assistance. Then a rigorous proof of the existence of an exact solution close to the numerical one is obtained by a fixed-point argument. The efficiency of this method is demonstrated with the examples of the fourth order Gelfand- and Emden-equations on various domains.

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Borbála Fazekas was born in Debrecen, Hungary in 1978. She has completed her PhD under the supervision of Michael Plum at the KIT in Karlsruhe in 2012. She has been an assistant professor at the University of Debrecen since 2008. Her research interests are PDE´s with numerical methods.

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