Existence and non-existence, as well as qualitative properties, of nontrivial non-negative solutions for elliptic equations with singular potentials were recently studied by several authors, but, essentially, only with a solely critical exponent. The large literature on p-Laplacian equations in the entire R^n differs somehow for the nonlinear structure, objectives and methods from those presented in this paper. Indeed, the combination of the two critical exponents induces more subtleties and difficulties. When just one critical exponent is involved, there are solutions to the corresponding equations. In our context, very few is known: yet, we refer to an interesting approach by Kang and Li.
On a p-Laplace equation with multiple critical nonlinearities
FILIPPUCCI, Roberta;PUCCI, Patrizia;
2009
Abstract
Existence and non-existence, as well as qualitative properties, of nontrivial non-negative solutions for elliptic equations with singular potentials were recently studied by several authors, but, essentially, only with a solely critical exponent. The large literature on p-Laplacian equations in the entire R^n differs somehow for the nonlinear structure, objectives and methods from those presented in this paper. Indeed, the combination of the two critical exponents induces more subtleties and difficulties. When just one critical exponent is involved, there are solutions to the corresponding equations. In our context, very few is known: yet, we refer to an interesting approach by Kang and Li.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
