Infinitely many solutions for a class of quasilinear equation with a combination of convex and concave terms - Teng, Kaimin; Agarwal, Ravi P. (Topological Methods in Nonlinear Analysis, 2017)
We consider the following quasilinear elliptic equation with convex and concave nonlinearities: equation* -Δ_p u-(Δ_pu^2)u+V(x)|u|^p-2u=λ K(x) |u|^q-2u+μ g(x,u),in R^N, equation* where 2≤ p< N, 1< q< p, λ,μR, V and K are potential functions, and gC(R^N×R,R) is a continuous function. Under some suitable conditions on V,K and g, the existence of infinitely many solutions is established.