The Research Group “Nonlinear Differential Equations” focuses its activities around a basic core: the qualitative and quantitative analysis of different types of differential equations, with an emphasis on problems arising in biology, physics or medicine, among many other branches of science or technology. More specifically, our group studies ordinary differential equations with singularities, discontinuities or impulses, along with many types of problems in which the usual differential operators are replaced with more general versions of them, such as fractional order derivatives. We also consider other kinds of derivatives by means of which the usual mathematical models can be improved by incorporating uncertainty, dead times or sudden changes.

Our main research lines are the following:

• Existence of solution for equations with singularities, discontinuities or impulses (by means of fixed point theorems for completely continuous or monotone operators, or by means of variational techniques).
• Constant sign solutions of nonlinear problems (through previous analysis of the Green’s functions of the corresponding linear problems).
• Qualitative analysis and optimal control in disease spread models.
• Existence and stability of solutions of ordinary or partial differential equations with impulses or with fractional order derivatives.
• Differential problems with nonlocal conditions (such as multipoint or integral conditions).
• Fuzzy or fractional differential equations.