The nonlinear (p,q)-Schrödinger equation with a general nonlinearity: Existence and concentration

We investigate the following class of (p,q)-Laplacian problems:{−εpΔpv−εqΔqv+V(x)(|v|p−2v+|v|q−2v)=f(v) in RN,v∈W1,p(RN)∩W1,q(RN),v>0 in RN, where ε>0 is a small parameter, N≥3, 10 and V0:=infΛ⁡V0 dans RN, où ε>0 est un petit paramètre, N≥3, 10 et V0:=infΛ⁡V