This thesis focuses on the nonlinear fourth order partial differential equation which can be used as a model of an asymmetrically supported beam or a generalized model of a suspension bridge. We present an overview of existing results for related problems. Then, the variational...

This paper deals with a BVP for a system which consists of two ordinary differential equations of the second order with concave and convex nonlinearities and Dirichlet boundary conditions. One of the equations contains a positive parameter $\lambda$. The aim of this work is&#x...

This thesis is devoted to the travelling wave solutions of the generalized Fisher-Kolmogorov equation with discontinuous density dependent diffusion that can degenerate or have singularities at equilibrium points. The reaction term is either bistable or monostable and it is a continuous, pos...

This thesis is devoted to studying of an eigenvalue problem of radially symmetric Laplace operator with a nonlocal (integral) boundary condition in general dimension $ n $. In addition, we are interested in describing the so-called Fučík spectrum of the corresponding problem.�...

In the present thesis, we study various versions of Thomassen's conjecture which says that every $4$-connected line graph is Hamiltonian. We show known partial results as well as well as disproving stronger conjectures.

The present thesis is motivated by the study of Chvátal's t_0-tough conjecture. We recall this conjecture in the context of Hamiltonian Graph Theory. We review partial results to the conjecture, and we analyse constructions which provide lower bounds to this conjecture and to s...

In this thesis we set ourselves the task to present regularity properties of mappings, basic results for them, and Newton-type methods for solving (generalized) equations. The Chapter 1 is divided into two sections. In the rst section, we motivated our considerations by�...

In recent years, the study of quaternions has become an active research area of applied geometry, mainly due to an elegant and efficient possibility to represent using them rotations in three dimensional space. Thanks to their distinguished properties, quaternions are often used in ...

This work concerns the solvability of the semi-linear elliptic partial differential equations at resonance with measure data in the very weak sense, i.e., the solution is an element of the space L^1(D). Particularly, we assume D to be a bounded domain in R^N with C^2 boun...

In this thesis we study rational techniques for computing exact/approximate parameterizations of canal and ringed surfaces. In the first part of the thesis we focus on canal surfaces given implicitly the designed approach is based on computing approximate topology-based parameterizations of&...

The author has asked for the recognition of diploma thesis as a doctoral (RNDr.) thesis. Annotation of diploma thesis: This master's thesis studies the problem of robust stabilization by static state and static output feedback. We look for an optimal feedback that assigns the&#...

This thesis focuses on bistable equation $u_t = \varepsilon^2 u_{xx} -F'(u)$ that models the dynamics of phase transition at some critical temperature. It is based on work of Drábek and Robinson (Drábek, P. and Robinson, S.B.: Continua of local minimizers in a non-smooth m...

The author has asked for the recognition of diploma thesis as a doctoral (RNDr.) thesis. Annotation of diploma thesis: This diploma thesis deals with the transport equation on semidiscrete domains. In the first part we focus on the linear equation. We present basic properties ...

The subject of the diploma thesis is the Heston model. One part of the thesis illustrates the complexity of the calibration process of the model. This is done using synthetic option prices, where the model implied parameters are known. Calibration of the model to the data...

In recent years, studying convolutions of hypersurfaces (especially of curves and surfaces) has become an active research area. For instance, one of the fundamental operations in Computer Aided Design, i.e., offsetting, can be expressed as the convolution with a circle/sphere. The main&...

This thesis is devoted to special techniques for interpolation of planar (points and associated tangent vectors) and spatial (quadrilateral mesh of points with associated normal vectors) data. In the first theoretical part, we study Hermite interpolation by cubic Pythagorean hodograph (PH)&...