Infinitely many solutions for quasilinear elliptic equations involving (p,q)(p,q)-Laplacian in RR

In this paper, under some superquadratic conditions made on the nonlinearity ff, we use variational approaches to establish the existence of infinitely many solutions to quasilinear elliptic equations with (p,q)(p,q)-Laplacian −Lpu−Lqu+a(x)|u|p−2u+b(x)|u|q−2u=f(x,u)inR, where 1