Bernstein approximations of Dirichlet problems for elliptic operators on the plane.
Bifurcation of solutions of nonlinear Sturm-Liouville problems.
Approximation of solutions to second order nonlinear Picard problems with Carathéodory right-hand side
We present an approximation method for Picard second order boundary value problems with Carathéodory righthand side. The method is based on the idea of replacing a measurable function in the right-hand side of the problem with its Kantorovich polynomial. We will show that this approximation scheme recovers essential solutions to the original BVP. We also consider the corresponding finite dimensional problem. We suggest a suitable mapping of solutions to finite dimensional problems to piecewise constant...
Applications of global bifurcation to existence theorems for Sturm-Liouville problems
Numerical detection of bifurcation point in the curve
We are presenting a numerical method which detects the presence and position of a bifurcation simplex, the regular -dimensional simplex, which may be considered as “fat bifurcation point”, in the curve of zeroes of the map . On the other hand the bifurcation simplex appears in the neighbourhood of the bifurcation point, meaning that we have the method to locate the bifurcation point as well. The method does not require any estimation of the derivative of the function and refers to the values...
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