The stability question of the Lane-Emden stationary gaseous star configurations is an interesting problem arising in astrophysics. We establish both linear and nonlinear dynamical instability results for the Lane-Emden solutions in the framework of the Navier-Stokes-Poisson system with adiabatic exponent 6/5 < γ < 4/3.

In this article, we apply blow-up analysis to study pointwise a priori estimates for some p-Laplacian equations based on Liouville type theorems. With newly developed techniques, first extend the classical results of interior gradient harmonic function that p-harmonic function, i.e., solution Δpu = 0, x ∈ Ω. We then obtain singularity and decay sign-changing Lane-Emden-Fowler equation −Δpu |u|λ...

The ultimate goal of this study is to develop a numerically effective approximation technique acquire numerical solutions the integer and fractional-order Bratu singular Lane–Emden-type problems especially with exponential nonlinearity. Both initial boundary conditions were considered fractional derivative being in Liouville–Caputo sense. In direct approach, generalized Bessel matrix method bas...

Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as across almost all natural and engineering sciences. Although several excellent standard software packages are available for ODEs, there are for good reasons no standard numerical continuation toolboxes available for parti...

Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In ...