论文标题
缺乏规律性和没有Ambrosetti-Rabinowitz条件的分数Orlicz问题的基态和淋巴结溶液
Ground state and nodal solutions for fractional Orlicz problems with lack of regularity and without the Ambrosetti-Rabinowitz condition
论文作者
论文摘要
我们考虑了由分数orlicz g-laplace操作员驱动的非本地shrödinger问题，如下所示\ begin {qore {equination} \ label {pp}（ - \ triangle_ {g}）^αu+g（u）= k（u）= k（x） \ Mathbb {r}^{d}，\ tag {p} \ end {qore}其中$ d \ geq 3，\（ - \ triangle_ {g}）^α$是分数orlicz g-laplace Operator，$ \ mathbb {r} $是一个可测量的函数，$ k $是一个积极的连续功能。采用Nehari歧管方法，并且不假设众所周知的Ambrosetti-Rabinowitz和在非线性项$ f $上的可不同性条件，我们证明问题\ eqref {pp}具有固定符号的基础状态和节点（或签名）解决方案。
We consider a non-local Shrödinger problem driven by the fractional Orlicz g-Laplace operator as follows \begin{equation}\label{PP} (-\triangle_{g})^αu+g(u)=K(x)f(x,u),\ \ \text{in}\ \mathbb{R}^{d},\tag{P} \end{equation} where $d\geq 3,\ (-\triangle_{g})^α$ is the fractional Orlicz g-Laplace operator, $f:\mathbb{R}^d\times\mathbb{R}\rightarrow \mathbb{R}$ is a measurable function and $K$ is a positive continuous function. Employing the Nehari manifold method and without assuming the well-known Ambrosetti-Rabinowitz and differentiability conditions on the non-linear term $f$, we prove that the problem \eqref{PP} has a ground state of fixed sign and a nodal (or sign-changing) solutions.
