论文标题
晶格图上的一类半线性椭圆方程
A class of semilinear elliptic equations on lattice graphs
论文作者
论文摘要
在本文中，我们研究表格的半连续椭圆方程{eqnArray*}-ΔU+a（x）| u |^{p-2} u |^b（x）| u |^{q-2} u = 0 \ end end \ end en \ end {eqnArray {eqnarray {eqnArray*} $ 2 \ leq p <q <+\ infty $。根据Brézis-lieB的引理和浓度紧凑性原理，我们证明了上述方程的积极解决方案，并具有恒定系数$ \ bar {a}，\ bar {b} $，\ bar {b} $以及有限的palais palais-male序列的分解，用于函数nignigents parais-smale sements in the bar bar bar bar bar} 分别。
In this paper, we study the semilinear elliptic equation of the form \begin{eqnarray*} -Δu+a(x)|u|^{p-2}u-b(x)|u|^{q-2}u=0 \end{eqnarray*} on lattice graphs $\mathbb{Z}^{N}$, where $N\geq 2$ and $2\leq p<q<+\infty$. By the Brézis-Lieb lemma and concentration compactness principle, we prove the existence of positive solutions to the above equation with constant coefficients $\bar{a},\bar{b}$ and the decomposition of bounded Palais-Smale sequences for the functional with variable coefficients, which tend to some constants $\bar{a},\bar{b}$ at infinity, respectively.
