Exact multiplicity of positive solutions for a class of second-order two-point boundary problems with weight function.
In this note we propose an exact simulation algorithm for the solution of (1)d X t = d W t + b̅ ( X t ) d t, X 0 = x, where b̅is a smooth real function except at point 0 where b̅(0 + ) ≠ b̅(0 −) . The main idea is to sample an exact skeleton of Xusing an algorithm deduced from the convergence of the solutions of the skew perturbed equation (2)d X t β = d W t + b̅ ( X t β ) d t + β d L t 0 ( X β ) , X 0 = x towardsX solution of (1) as β ≠ 0 tends to 0. In this note, we show that this convergence...
The example is constructed of the C1-smooth skew product of interval maps possessing the one-dimensional ramified continuum (containing no arcs homeomorphic to the circle) with an infinite set of ramification points as the global attractor.
A bifurcation problem for variational inequalities is studied, where is a closed convex cone in , , is a matrix, is a small perturbation, a real parameter. The main goal of the paper is to simplify the assumptions of the abstract results concerning the existence of a bifurcation of periodic solutions developed in the previous paper and to give examples in more than three dimensional case.
This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space