Perturbations of planar quasilinear differential systems

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

“…Assume that γ < µ σ,p . Let u be a nontrivial solution of problem (2)- (3). Then equation( 12), has two real roots λ 1 , λ 2 with 0 < λ 1 < λ 2 and the following points hold: (i) if r 0 u ′ (r 0 ) = (λ i − σ)u(r 0 ) fore some i ∈ {1, 2}, then u(r) = u(r 0 )r σ−λ i 0 r λ i −σ , r > 0.…”

“…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).…”

“…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.…”