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.
1996
7
1
171
185
http://www-users.mat.umk.pl/~tmna/.../v07n1-07.pdf
Musina, Roberta
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32652
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