1 citations · 1 across the 9 of their papers we have counts for
10 papers
Generalized Kolmogorov systems with applications to astrophysics and biology
Dorota Bors, Robert Stańczy
We consider generalized Kolmogorov system. We prove the existence of heteroclinic trajectory. We apply the results to astrophysical models for self-gravitating particles and predat…
Dynamical system describing cloud of particles in relativistic and non-relativistic framework
Robert Stańczy, Dorota Bors
We consider fairly general class of dynamical systems under the assumptions guaranteeing the existence of Lyapunov function around some nontrivial stationary point. Moreover, the e…
Tolman-Oppenheimer-Volkoff Equation
Dorota Bors, Robert Stańczy
The existence of solutions to Tolman-Openheimer-Volkoff equation with linear equation of state modeling relativistic cloud of interacting particles is proved for mass parameter bel…
Dynamical system modeling fermionic limit
Dorota Bors, Robert Stańczy
The existence of multiple radial solutions to the elliptic equation modeling fermionic cloud of interacting particles is proved for the limiting Planck constant and intermediate va…
Vapor-liquid equilibrium (VLE) properties versus critical exponent theory - on new approximate mathematical approach to determine the critical exponent value of the vapor-liquid coexistence curve
Beata Staśkiewicz, Robert Stańczy
A novel mathematical rigorous method to obtain the vapor-liquid equilibrium curves near the critical point has been proposed covering the cases of well-known and commonly used equa…
Global invertibility and implicit function theorems by mountain pass theorem
Dorota Bors, Robert Stańczy
We formulate some global invertibility and implicit function theorems. We extend the result of Idczak, Skowron and Walczak on the invertibility of the operators to the case of the…
Some nonlinear second order equation modelling rocket motion
Dorota Bors, Robert Stańczy
In this paper, we consider a nonlinear second order equation modelling rocket motion in the gravitational field obstructed by the drag force. The proofs of the main results are bas…
Multiple solutions for equations involving bilinear, coercive and compact forms with applications to differential equations
Robert Stańczy
The existence of multiple fixed points for the coercive, bilinear, compact forms defined in the cone in the Banach space. Multiple applications to the integral equations derived fr…
On stationary solutions to reaction-diffusion equations with nonlocal term
Robert Stańczy
In this paper we obtain the existence of a radial solution for some elliptic nonlocal problem with constraints. The problem arises from some reaction-diffusion equation modelling a…
On an evolution system describing self-gravitating particles in microcanonical setting
Robert Stańczy
The global in time existence of solutions of a system describing the interaction of gravitationally attracting particles with a general diffusion term and fixed energy is proved. T…