Existence and multiplicity of solutions for a p-Kirchhoff equation on R N ${\mathbb {R}}^{N}$
Existence and multiplicity of solutions for a p-Kirchhoff equation on R N ${\mathbb {R}}^{N}$
In this paper, we consider the following p-Kirchhoff equation: P $$\begin{aligned} \bigl[M\bigl( \Vert u \Vert ^{p}\bigr)\bigr]^{p-1} \bigl(-\Delta_{p} u+V(x) \vert u \vert ^{p-2}u \bigr)=f(x,u), \quad x\in{\mathbb {R}}^{N}, \end{aligned}$$ where $f(x,u)=\lambda g(x)|u|^{q-2}u+h(x)|u|^{r-2}u,1< q< p< r< p^{*}$ ( $p^{*}=\frac{Np}{N-p}$ if $N\ge p,p^{*}=\infty$ if $N\le p$ ). Using variational methods, we prove that, under …