We consider the problem of non-existence of solutions for the following Hénon-Lane-Emden system  −∆u = |x|v in R , −∆v = |x|u in R , when pq > 1, p, q, a, b ≥ 0, and (p, q) are under the critical hyperbola, i.e. N+a p+1 + N+b q+1 > N − 2. We show that there is no positive bounded solution in dimension N = 3, extending a result established recently by Phan-Souplet in the scalar case. This solve...

The wavelets have many applications in engineering and the sciences, especially mathematics. Recently, 2021, wavelet Boubaker (WB) polynomials were used for first time to study their properties detail. They also utilized solving Lane-Emden equation. aim of this paper is show truncated Wavelet variation problems. In research, direct method using was presented variational reduces problem into a s...

Using the scalar and tensor virial equations, the Lane-Emden equation expressing the hydrostatic equilibrium and small oscillations around the equilibrium, we show how the cosmological constant Λ affects various astrophysical quantities important for large matter conglomeration in the universe. Among others we examine the effect of Λ on the polytropic equation of state for spherically symmetric...

We are concerned with proving that solutions of certain dynamical systems on time scales satisfy some monotoneity conditions. These results then give important results for nth order linear scalar equations. We then give a related result for a third order nonlinear (Emden–Fowler type) dynamic equation.