Existence and Global Behavior of Decaying Solutions of a Nonlinear Elliptic Equation

On the radial solutions of a p-Laplace equation with the Hardy potential

“…where 2 < p < N and h is a radial function on R N − {0} such that h(|x|) = γ|x| −p with γ > 0. This equation has been studied by several authors, see in particular the survey given in [1][2][3][4][5][6][7][8] where h(|x|) = γ|x| −ν with γ = 0 and ν > 0. The purpose of this article is to apply some results obtained in [5] to equation (1).…”

“…This equation has been studied by several authors, see in particular the survey given in [1][2][3][4][5][6][7][8] where h(|x|) = γ|x| −ν with γ = 0 and ν > 0. The purpose of this article is to apply some results obtained in [5] to equation (1). More precisely, we combine some elements of this approach with others from dynamical systems theory, in particular the techniques developed by [1][2][3]8] for the p-Laplacian problem.…”

“…The purpose of this article is to apply some results obtained in [5] to equation (1). More precisely, we combine some elements of this approach with others from dynamical systems theory, in particular the techniques developed by [1][2][3]8] for the p-Laplacian problem. We use a Fowler-type transformation, introduced in [1,2,9], which establishes a bijective relationship between radial solutions and those of a two-dimensional dynamical system.…”

“…More precisely, we combine some elements of this approach with others from dynamical systems theory, in particular the techniques developed by [1][2][3]8] for the p-Laplacian problem. We use a Fowler-type transformation, introduced in [1,2,9], which establishes a bijective relationship between radial solutions and those of a two-dimensional dynamical system. Using these techniques, we provide an explanation of the asymptotic behavior which strongly depends on the characteristic equation of the dynamical system obtained from radial version of equation (1) using the logarithmic change.…”