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 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 ...
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 ...
De Marchis, F., Ianni, I., Pacella, F.: A Morse index formula for radial solutions of Lane–Emden problems. Adv. Math. 322, 682–737 (2017) Google Scholar Gidas, B., Spruck, J.: A priori bounds for positive solutions of nonlinear elliptic equations. Commun. Partial Differ. Equ....
It is shown in a numerical experiment that this formula is more efficient than the Majorana formula. For the solution of the Cauchy problem with a positive derivative at the origin, a parametrization is obtained that ensures that the boundary conditions of the singular boundary value problem on ...
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 ...
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 ...
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 ...
We prove several asymptotic formulae as the nonlinear exponent gets large.Sadaf, HabibiTakahashi, FutoshiDiscrete & Continuous Dynamical Systems: Series A
A monotonicity formula and a Liouville-type theorem for a fourth order supercritical problem 2014, Advances in Mathematics Show abstract Liouville-type theorems and bounds of solutions of Hardy-Hénon equations 2012, Journal of Differential Equations Show abstract Lane-Emden systems with negative exponents...