Publication Date:
2016-07-27
Description:
We consider the p -Laplacian problem − ε p Δ p u + V ( x ) u p − 2 u = f ( u ) , u ∈ W 1 , p ( R N ) , where p ∈ (1, N ) and f ( s ) is of critical growth. In this paper, we construct a single peak solution around an isolated component of the positive local minimum points of V as ε → 0 with a general nonlinearity f . In particular, the monotonicity of f ( s )/ s p −1 and the so-called Ambrosetti-Rabinowitz condition are not required.
Print ISSN:
0022-2488
Electronic ISSN:
1089-7658
Topics:
Mathematics
,
Physics