Project R-15336

Sliding limit cycles in regularized planar piecewise smooth systems and delay equations with state-dependent delays (Research)

The main goal of this project is to study the existence and number of sliding limit cycles in regularized planar piecewise smooth systems. We deal with a visible-invisible tangency point of any even contact order. This is a significant generalization of the well-known case with a visible-invisible two-fold. We give a simple criterion, expressed in terms of the slow divergence integral, for the existence and number of sliding limit cycles in such regularized systems. We also study sliding limit cycles of regularized piecewise linear systems near identically zero slow divergence integral. Also, this project intends to prove bifurcation results and almost periodic solutions for Functional Volterra-Stieltjes integral equations, through the degree theory. Further, the idea is to extend the results for these equations to other types of equations such as impulsive functional Volterra-Stieltjes integral equations and functional Volterra-Stieltjes delta integral equation on time scales. The final part of the project intends to investigate the pullback attractors to abstract functional differential equation with statedependent delays and to apply them to partial differential equations.

21 November 2024 - 31 March 2027