标题： 分数Orlicz Sobolev空间中一种非局部类型问题的基态解 显示英文标题

标题： Ground state solutions for a non-local type problem in fractional Orlicz Sobolev spaces

摘要： 在本文中，我们研究如下在分数Orlicz-Sobolev空间中的非局部问题 \begin{eqnarray*} (-\Delta_{\Phi})^{s}u+V(x)a(|u|)u=f(x,u),\quad x\in\mathbb{R}^N, \end{eqnarray*} 其中 $(-\Delta_{\Phi})^{s}(s\in(0, 1))$表示非局部且可能非齐次的算子，即所谓的分数 $\Phi$-Laplacian。 在不假设非线性项满足Ambrosetti-Rabinowitz型条件和Nehari型条件的情况下，我们在周期情形下获得了上述问题的基态解的存在性。 证明基于山路定理的一个变体版本以及分数Orlicz Sobolev空间的一个Lions型结果。 显示英文摘要

摘要： In this paper, we study the following nonlocal problem in fractional Orlicz Sobolev spaces \begin{eqnarray*} (-\Delta_{\Phi})^{s}u+V(x)a(|u|)u=f(x,u),\quad x\in\mathbb{R}^N, \end{eqnarray*} where $(-\Delta_{\Phi})^{s}(s\in(0, 1))$ denotes the non-local and maybe non-homogeneous operator, the so-called fractional $\Phi$-Laplacian. Without assuming the Ambrosetti-Rabinowitz type and the Nehari type conditions on the nonlinearity, we obtain the existence of ground state solutions for the above problem in periodic case. The proof is based on a variant version of the mountain pass theorem and a Lions' type result for fractional Orlicz Sobolev spaces.