Nonlinear perturbations of a periodic Kirchhoff equation in RNRN

This paper is concerned with the existence of positive solutions for the following class of nonlocal problem M(∫RN|∇u|2dx+∫RNV(x)|u|2dx)[−Δu+V(x)u]=λf(u)+γuτinRN, where τ=5τ=5 for N=3N=3 and τ∈(1,+∞)τ∈(1,+∞) for N=1,2N=1,2, λλ is a positive parameter and γ∈{0,1}γ∈{0,1}. Moreover, MM, VV, and ff are continuous functions satisfying some conditions.