TY - JOUR
T1 - A positive solution for an asymptotically linear elliptic problem on ℝn autonomous at infinity
AU - Jeanjean, Louis
AU - Tanaka, Kazunaga
PY - 2002/8
Y1 - 2002/8
N2 - In this paper we establish the existence of a positive solution for an asymptotically linear elliptic problem on ℝn. The main diffculties to overcome are the lack of a priori bounds for Palais-Smale sequences and a lack of compactness as the domain is unbounded. For the first one we make use of techniques introduced by Lions in his work on concentration compactness. For the second we show how the fact that the “Problem at infinity” is autonomous, in contrast to just periodic, can be used in order to regain compactness.
AB - In this paper we establish the existence of a positive solution for an asymptotically linear elliptic problem on ℝn. The main diffculties to overcome are the lack of a priori bounds for Palais-Smale sequences and a lack of compactness as the domain is unbounded. For the first one we make use of techniques introduced by Lions in his work on concentration compactness. For the second we show how the fact that the “Problem at infinity” is autonomous, in contrast to just periodic, can be used in order to regain compactness.
KW - Asymptotically linear problems in ℝ
KW - Elliptic equations
KW - Lack of compactness
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U2 - 10.1051/cocv:2002068
DO - 10.1051/cocv:2002068
M3 - Article
AN - SCOPUS:0036414880
VL - 7
SP - 597
EP - 614
JO - ESAIM - Control, Optimisation and Calculus of Variations
JF - ESAIM - Control, Optimisation and Calculus of Variations
SN - 1292-8119
ER -