ON A CLASS OF QUASILINEAR SCHRODINGER EQUATIONS WITH VANISHING POTENTIALS AND MIXED NONLINEARITIES

In this paper, we study the following generalized quasilinear Schrodinger equations with mixed nonlinearity {-div(g(2)(u)del u) + g(u)g'(u)vertical bar del u vertical bar(2)+ V(x)u - K (x)f (u) + gimel xi(x)g(u)vertical bar G(u)vertical bar(p-2)G(u), x is an element of R-N, u is an element of D-1,D-2(R-N), where N >= 3, V;K are nonnegative continuous functions and f is a continuous function with a quasicritical growth. Using a change of variable as G(u) = integral(u)(0) g(t)dt, the above quasilinear equation is reduced to a semilinear one. Under some suitable assumptions, we prove that the above equation has at least one nontrivial solution by working in weighted Sobolev spaces and employing the variational methods.