The proposed algorithm first discretizes the fractal-fractional differentiation by using the finite difference formula in the time direction. Then, it simplifies the original equation to the recurrent equations by expanding the unknown solution in terms of the 2D CPs and using ...
MAIN RESULTS In this Section, by using the Riccati transformation technique and the formula 1 (xγ(t))∆ = γ [hxσ + (1 − h)x]γ−1 dhx∆(t), 0 which is a simple consequence of Keller's chain rule [5, Theorem 1.90], we will establish some new sufficient conditions for...
We derive monotonicity formulae for solutions of the fractional Hénon–Lane–Emden equation(−Δ)su=|x|a|u|p−1uinℝn,when00andp>1. Then, we ... M Fazly,J Wei - 《Communications in Contemporary Mathematics》 被引量: 12发表: 2016年 Exact first integrals for a Lane–Emden ...
Finally, to prove that pup(x) converges to γlog|x|, which is the last part of Theorem 2, let us use the representation formulapup(x)=p∫BG(x,y)|up(y)|p−1up(y)dy=p[−∫{|y|⩽rp}G(x,y)|up(y)|pdy+∫{rp<|y|<1}G(x,y)|up(y)|pdy] where G(x,y) is the ...
On stable solutions of the fractional Henon-Lane-Emden equation We derive monotonicity formulae for solutions of the fractional Henon-Lane-Emden equation MWJ Fazly - 《Communications in Contemporary Mathematics》 被引量: 0发表: 2016年 On stable solutions of the fractional Henon-Lane-Emden equation ...
A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem 2014, Advances in Mathematics Show abstract Some Liouville theorems for Hénon type elliptic equations 2012, Journal of Functional Analysis Show abstract Finite Morse index solutions of an elliptic equation with ...
The proposed algorithm first discretizes the fractal–fractional differentiation by using the finite difference formula in the time direction. Then, it simplifies the original equation to the recurrent equations by expanding the unknown solution in terms of the 2D CPs and using the -weighted finite ...
Starting from Green's formula, the generalized solution of a boundary value problem is defined, and two ... Zhitarashu,N V - 《Mathematics of the Ussr Sbornik》 被引量: 6发表: 1987年 Effects of ceramic processing parameters on the microstructure and dielectric properties of \\hbox{(Ba}_{...
We derive monotonicity formulae for solutions of the fractional Hénon–Lane–Emden equation(−Δ)su=|x|a|u|p−1uinℝn,when0 0andp>1. Then, we apply these formulae to classify stable solutions of the above equation.doi:10.1142/S021919971650005XMostafa FazlyJuncheng WeiWorld Scientific ...
A class of second derivative backward differentiation formula is derived from some continuous multistep schemes using the multistep collocation technique. The tech-nique transforms the numerical methods to a system of non-linear equations represented as a tridiagonal matrix, thereby obtaining numerical ...