In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application, obtain nonexistence nontrivial (not necessarily positive) radial solutions the Lane-Emden system posed in ball, critical and supercritical regimes. Some our results also apply to general fully nonlinear operators, su...

This paper is devoted to proposing numerical algorithms based on the use of tau and collocation procedures, two widely used spectral approaches for treatment initial high-order linear non-linear equations singular type, especially those Emden–Fowler type. The class modified Chebyshev polynomials third-kind constructed. generalizes polynomials. A new formula that expresses first-order derivative...

Monte Carlo (MC) method played an essential role in many areas of human activity and has found application branches physical science. This paper proposes a computational technique based on MC algorithms to solve Lane–Emden (LE) type equations. We analyze four LE equations arising astrophysics: the positive negative indices polytropic gas spheres, isothermal sphere, white dwarf equation. calcula...

The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of the proof to partial differential equations is straight forward. The method, whose mathematical basis in physics was discussed recently by one of the present ...

Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these were found. For every type complete list nonequivalent is issued. As exampes equivalence problem for Painleve II equation, III equation with three zero parameters, Emden and some other solved.