Infinitely many solutions for quasilinear Schrödinger equation with critical exponential growth in RNRN

This paper shows the existence of infinitely many solutions for the quasilinear equations of the formequation(0.1)−△Nu+V(x)|u|N−2u−△N(u2)u=λK(x)|u|q−2u+h(u),   x∈RN,−△Nu+V(x)|u|N−2u−△N(u2)u=λK(x)|u|q−2u+h(u),   x∈RN, where △Nu△Nu is the N  -Laplacian operator, N≥3N≥3, λ≥0λ≥0, 10λ0>0 such that problem (0.1) admits infinitely many high-energy solutions provided that λ∈[0,λ0]λ∈[0,λ0].