We provide the structure of regular/singular fast/slow decay radially symmetric solutions for a class of superlinear elliptic equations with an indefinite weight. In particular we are interested in the case where such a weight is positive in a ball and negative outside, or in the reversed situation. We extend the approach to elliptic equations in presence of Hardy potentials, i.e. to $$Delta u +rac{h(| extrm{x}|)}{| extrm{x}|^2} u+ f(u, | extrm{x}|)=0 $$ where $h$ is not necessarily constant. By the use of Fowler transformation we study the corresponding dynamical systems, presenting the construction of invariant manifolds when the global existence of solutions is not ensured.
Franca, M., Sfecci, A. (2018). Entire Solutions of Superlinear Problems with Indefinite Weights and Hardy Potentials. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 30(3), 1081-1118 [10.1007/s10884-017-9589-z].
Entire Solutions of Superlinear Problems with Indefinite Weights and Hardy Potentials
FRANCA, Matteo
Membro del Collaboration Group
;
2018
Abstract
We provide the structure of regular/singular fast/slow decay radially symmetric solutions for a class of superlinear elliptic equations with an indefinite weight. In particular we are interested in the case where such a weight is positive in a ball and negative outside, or in the reversed situation. We extend the approach to elliptic equations in presence of Hardy potentials, i.e. to $$Delta u +rac{h(| extrm{x}|)}{| extrm{x}|^2} u+ f(u, | extrm{x}|)=0 $$ where $h$ is not necessarily constant. By the use of Fowler transformation we study the corresponding dynamical systems, presenting the construction of invariant manifolds when the global existence of solutions is not ensured.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
