Abstract :
We consider the nonlinear eigenvalue problem on an interval
−u (t )+ g u(t ) = λsin u(t ), u(t ) > 0, t ∈ I := (−T,T ), u(±T ) = 0,
where λ>0 is a parameter andT >0 is a constant. It is known that if λ 1, then the corresponding
solution uλ has boundary layers. In this paper, we establish an asymptotic expansion of the width of
the boundary layers of uλ when λ 1, which is explicitly represented by g and completely different
from that of the case where g ≡ 0.
2003 Elsevier Inc. All rights reserved
