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Electronic Journal of Differential Equations, Vol. 2004(2004), No. 76, pp. 132. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
 

Summary: Electronic Journal of Differential Equations, Vol. 2004(2004), No. 76, pp. 1­32.
ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu
ftp ejde.math.txstate.edu (login: ftp)
VARIATIONAL METHODS FOR A RESONANT PROBLEM
WITH THE p-LAPLACIAN IN RN
B´EN´EDICTE ALZIARY, JACQUELINE FLECKINGER, PETER TAK´AC
Abstract. The solvability of the resonant Cauchy problem
-pu = 1m(|x|)|u|p-2
u + f(x) in RN
; u D1,p
(RN
),
in the entire Euclidean space RN (N 1) is investigated as a part of the
Fredholm alternative at the first (smallest) eigenvalue 1 of the positive p-
Laplacian -p on D1,p(RN ) relative to the weight m(|x|). Here, p stands
for the p-Laplacian, m: R+ R+ is a weight function assumed to be radially
symmetric, m 0 in R+, and f : RN R is a given function satisfying a suit-
able integrability condition. The weight m(r) is assumed to be bounded and to
decay fast enough as r +. Let 1 denote the (positive) eigenfunction as-
sociated with the (simple) eigenvalue 1 of -p. If RN f1 dx = 0, we show

  

Source: Alziary-Chassat, Bénédicte - Université Toulouse 1 - Capitole

 

Collections: Mathematics