We address the solvability of critical Lane-Emden system in a smooth bounded domain with small spherical hole radius ϵ>0. prove that admits family positive solutions concentrate around center as ϵ→0, obtaining concrete qualitative description well. To best our knowledge, this is first existence result for on domain, while non-existence star-shaped domains has been known since early 1990s due to...

We prove the existence and uniqueness of stationary spherically symmetric positive solutions for the Schrödinger-Newton model in any space dimension d. Our result is based on a careful analysis of the corresponding system of second order differential equations. It turns out that d = 6 is critical for the existence of finite energy solutions and the equations for positive spherically symmetric s...

Based on the Solar Standard Model SSM we developed a solar model in hydrostatic equilibrium using two polytropes that describes both the radiative and convective zones of the solar interior. Then we apply small periodic and adiabatic perturbations on this bipolytropic model in order to obtain proper frequencies and proper functions. The frequencies obtained are in the p-modes range of low order...

We discuss the asymptotic behavior of solutions to a higher-order Emden–Fowler type equation with constant potential. Several author’s results are presented concerning both positive and oscillatory solutions to equations with regular and singular nonlinearities. We discuss the existence and asymptotic behavior of “blowup” solutions. Results on the asymptotic behavior of oscillating solutions ar...

We study the Emden-Fowler equation −∆u = |u|u on the hyperbolic space H . We are interested in radial solutions, namely solutions depending only on the geodesic distance from a given point. The critical exponent for such equation is p = (n + 2)/(n − 2) as in the Euclidean setting, but the properties of the solutions show striking differences with the Euclidean case. While the papers [23, 4] con...

Here, a simple method to determine the rate of convergence of Adomian decomposition method is introduced. The proposed method is used to compare between the rate of convergence of standard and modified (proposed by Wazwaz [A.M. Wazwaz, A new method for solving singular initial value problems in the second-order ordinary differential equations, Appl. Math. Comput. 128 (2002) 45–57]) Adomian meth...

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 ...