Multiple solutions to elliptic equations on $mathbb{R}^N$ with combined nonlinearities

摘要

In this paper, we are concerned with the multiplicity of nontrivial radial solutions for the following elliptic equation egin{equation*} egin{cases} - Delta u +V(x)u = -lambda Q(x)|u|^{q-2}u+ Q(x)f(u),quad xinmathbb{R}^N, u(x)ightarrow 0,quad hbox{as} |x|ightarrow +infty,end{cases} ag*{(P)$_lambda$} end{equation*} where $1