We consider a class of equations of the form -ε2 Δu + V (x)u = f(u), u ∈ H1 (RN). By variational methods, we show the existence of families of positive solutions concentrating around local minima of the potential V(x), as ε → 0. We do not require uniqueness of the ground state solutions of the associated autonomous problems nor the monotonicity of the function ξ → f(ξ)/ξ. We deal with asymptotically linear as well as superlinear nonlinearities.
|Number of pages||32|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 2004 Nov 1|
ASJC Scopus subject areas
- Applied Mathematics