My research aims at developing computer-assisted techniques for the study of Partial Differential Equations (PDEs). A rigorous usage of the machine provides powerful tools for the analysis of nonlinear equations, enabling the treatment of nontrivial problems. 

Using a combination of operator analysis and computer-assisted tools, I developed a methodology for proving constructively the existence of localized solutions in semi-linear PDEs and nonlocal equations on the whole space (i.e. R^m). Below is a list of applications with a selection of fine-looking solutions for which we established the existence.  For additional information about the general method, please refer to the following article.