Multiple solutions for a quasilinear Schrödinger equation on $\mathbb{R}^{N}$}

The multiplicity of positive weak solutions for a quasilinear Schrödinger equations $-L_p u +(λA(x)+1)|u|^{p-2}u= h(u)$ in $\mathbb{R}^N$ is established, where $L_p u\doteq ε^{p}Δ_p u +ε^{p}Δ_p (u^2)u$, $A$ is a nonnegative continuous function and nonlinear term $h$ has a subcritical growth. We achieved our results by using minimax methods and Lusternik-Schnirelman theory of critical points.

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