Infinitely many solutions to quasilinear Schrödinger system in RNRN

In this work, we study the existence of multiple solutions to the quasilinear Schrödinger system equation(0.1){−Δpu+a(x)|u|p−2u=κd−1Fu(x,u,v)+λ|u|m−2u,x∈RN,−Δqv+b(x)|v|q−2v=κd−1Fv(x,u,v)+μ|v|m−2v,x∈RN,u∈W1,p(RN),v∈W1,q(RN), where N≥3,10N≥3,10 and m,d∈(q,p∗),κ∈Rm,d∈(q,p∗),κ∈R. The potential functions a(x),b(x)∈L∞(RN)a(x),b(x)∈L∞(RN) are positive in RNRN. A major point is that we use the technique in Chen (2015) to verify the (PS)(PS) conditions and then apply a version of mountain pass lemma to prove the existence of infinitely many solutions of system (0.1).