In this paper we consider the nonlinear differential equation of the second order, which is known in applications as Thomas-Fermi equation. We deal with setting the conditions under which this equation exhibits singularity in interval (0, ∞). In the available literature, the authors investigate the singularity of the above equation at point 0, using numerical solution methods. The investigated equation has a wide application in quantum mechanics. Thomas-Fermi equation represents models atomic ions with a finite charge cloud and an overall positive charge. The boundary of the charge cloud is defined by the condition y(x) = 0, where y(x) represents the charge density at a given point x. We illustrate the existence of singular solutions numerically with two examples. In addition, to its use in quantum mechanics, the equation has potential applications in biochemistry. For example, if the atomic ions, e.g. sodium and chlorine ions penetrate the bacterium, they can cause the death of the bacterium.

Acknowledgement: The authors appreciate the VEGA Grant Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic and the Slovak Academy of Sciences for supporting this work under Grant No. 1/0423/23 and KEGA Grant 025 \v ZU-4/2024.