论文标题
径向准线性椭圆形问题，具有单数或消失的电位
Radial quasilinear elliptic problems with singular or vanishing potentials
论文作者
论文摘要
在本文中，我们继续我们在Arxiv：1912.07537开始的工作。给定$ 1 <p <n $，两个可测量的函数$ v \ left（r \右）\ geq 0 $和$ k \ left（r \右）> 0 $，以及连续函数$ a（r）> 0 \（r）> 0 \（r> 0）$ u |^{p-2} \ nabla u \右） +v \ left（\ left | x \右| \ right）| u |^{p-2} u = k（| x |）f（| x |）无穷大。我们通过应用变异方法发现了非负解的存在，为此，我们需要研究合适函数空间$ x $嵌入到lebesgue Space Spaces $ L_ {K}^k}^{q_ {1}}}+l_ {k}+l_ {k}^k}^Q_ {q_ {q_ {q_ {q_ {2} $中的紧凑性。非线性具有双功率超级$ P $ - 线性行为，为$ f（t）= \ min \ left \ left \ {t^{q_1 -1 -1}，t^{q_2 -1} \ right \} $，$ q_1，q_2> p $关于\ cite {avk_i}，在本文中，我们假设$ v $上的更多假设，我们能够放大一个值$ q_1，q_1，q_2 $，以获取其存在结果。
In this paper we continue the work that we began in arXiv:1912.07537. Given $1<p<N$, two measurable functions $V\left(r \right)\geq 0$ and $K\left(r\right)> 0$, and a continuous function $A(r) >0\ (r>0)$, we consider the quasilinear elliptic equation \[ -\mathrm{div}\left(A(|x| )|\nabla u|^{p-2} \nabla u\right) +V\left( \left| x\right| \right) |u|^{p-2}u= K(|x|) f(u) \quad \text{in }\mathbb{R}^{N}, \] where all the potentials $A,V,K$ may be singular or vanishing, at the origin or at infinity. We find existence of nonnegative solutions by the application of variational methods, for which we need to study the compactness of the embedding of a suitable function space $X$ into the sum of Lebesgue spaces $L_{K}^{q_{1}}+L_{K}^{q_{2}}$. The nonlinearity has a double-power super $p$-linear behavior, as $f(t)= \min \left\{ t^{q_1 -1}, t^{q_2 -1} \right\}$ with $q_1,q_2>p$ (recovering the power case if $q_1=q_2$). With respect to \cite{AVK_I}, in the present paper we assume some more hypotheses on $V$, and we are able to enlarge the set of values $q_1 , q_2$ for which we get existence results.
