From the viewpoint of the calculus of variations, the perturbed Kazdan-Warner problem: (1) −∆u+λu=k(x)u^{p−1}, u>0 in R^n, u→0 at ∞, where n≥3 and p>1 is subcritical. Problem (1) is studied with regard of the effect of the set M on topology of the energy sub levels: in the main results it is shown that the Lyusternik-Schnirelman category of M can affect the number of positive solutions to (1) in case p is close enough to the critical Sobolev exponent.
Multiple positive solutions of a scalar field equation in R^n
Musina, Roberta
1996-01-01
Abstract
From the viewpoint of the calculus of variations, the perturbed Kazdan-Warner problem: (1) −∆u+λu=k(x)u^{p−1}, u>0 in R^n, u→0 at ∞, where n≥3 and p>1 is subcritical. Problem (1) is studied with regard of the effect of the set M on topology of the energy sub levels: in the main results it is shown that the Lyusternik-Schnirelman category of M can affect the number of positive solutions to (1) in case p is close enough to the critical Sobolev exponent.File in questo prodotto:
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