Generalization of p-regularity notion and tangent cone description in the singular case

The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions

Application of p-regularity theory to the Duffing equation

Abstract The paper studies a solution existence problem of the nonlinear Duffing equation of the form F ( x , μ , β ) = x ″ + x + μ x 3 − β sin t = 0 , β > 0 , μ ≠ 0 , $$F(x,\mu, \beta)=x''+x+\mu x^{3}-\beta\sin t = 0,\quad \beta > 0, \mu\neq0,$$ where F : C 2 [ 0 , 2 π ] × R × R → C [ 0 , 2 π ] $F: \mathcal{C}^{2}[0,2\pi]\times\mathbb{R}\times \mathbb{R}\rightarrow\mathcal{C}[0,2\pi]$ and x ( 0 ) = x ( 2 π ) = 0 $x(0)=x(2\pi)=0$ using the p-regularity theory

P-regular nonlinear dynamics

In this paper we generalize the notion of $p$-factor operator which is the basic notion of the so-called $p$-regularity theory for nonlinear and degenerated operators. We prove a theorem related to a new construction of $p$-factor operator. The obtained results are illustrated by an example concerning nonlinear dynamical system

Generalization of p-regularity notion and tangent cone description in the singular case

The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions

Solutions to some singular nonlinear boundary value problems

We apply the so-called $p$-regularity theory to prove the existence of solutions to two nonlinear boundary value problems: an equation of rod bending and some nonlinear Laplace equation