Normal vectors of a surface are essential in various geometry-related applications. Since a normal vector at a point on a parametric surface is computed by a cross product of two tangent vectors at the point, a regular parametric surface may possess a degenerate normal vector at a point when tangent vectors of the surface are linearly dependent at the point. This paper describes an algorithm wh...

We consider a slightly subcritical Dirichlet problem with non-power nonlinearity in bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of solutions as case power-type nonlinearities. Instead, we use Ljapunov-Schmidt reduction method show that there is positive solution which concentrates at non-degenerate critical point Robin function....

Abstract We consider the harmonic heat flow for maps from a compact Riemannian manifold into that is complete and of non-positive curvature. prove if converges to limiting map non-degenerate critical point energy functional, then rate convergence exponential (in $$L^2$$ L 2 </mml:m...

employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of neumann two-point boundary valuesturm-liouville type equations. using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.

In a dialogue procedure the decision maker has to determine in each step the aspiration and reservation level expressing his wishes (goals). This leads to an optimization problem which is not easy to solve in the nonconvex case (the known starting point is not feasible). We propose a modiied standard embedding (one parametric optimization). This problem will be discussed from the point of view ...

An autonomous system of ordinary differential equations in the plane with a centre-saddle bifurcation is considered. The influence time damped perturbations power-law asymptotics investigated. particular solutions tending at infinity to fixed points limiting are stability these analyzed when parameter unperturbed takes critical and non-critical values. Conditions that ensure persistence perturb...