TY - JOUR
T1 - Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities
AU - Jeanjean, Louis
AU - Tanaka, Kazunaga
PY - 2004/11
Y1 - 2004/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=7244258733&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=7244258733&partnerID=8YFLogxK
U2 - 10.1007/s00526-003-0261-6
DO - 10.1007/s00526-003-0261-6
M3 - Article
AN - SCOPUS:7244258733
SN - 0944-2669
VL - 21
SP - 287
EP - 318
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 3
ER -