Ground State Solutions for a Non-Local Type Problem in Fractional Orlicz Sobolev Spaces

被引：0

作者：

Wang, Liben ^{[1
]}

Zhang, Xingyong ^{[2
]}

Liu, Cuiling ^{[2
]}

机构：

[1] Dongguan Univ Technol, Sch Comp Sci & Technol, Dongguan 523808, Peoples R China

[2] Kunming Univ Sci & Technol, Fac Sci, Kunming 650500, Peoples R China

来源：

AXIOMS | 2024年 / 13卷 / 05期

关键词：

fractional Orlicz-Sobolev spaces; fractional Phi-Laplacian; critical point; ground state; NONLINEAR SCHRODINGER-EQUATIONS; P-LAPLACIAN EQUATIONS; R-N; EXISTENCE;

D O I：

10.3390/axioms13050294

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the following non-local problem in fractional Orlicz-Sobolev spaces: (-Delta Phi)su+V(x)a(|u|)u=f(x,u), x is an element of RN, where (-Delta Phi)s(s is an element of(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 non-linearity f, we obtain the existence of ground state solutions for the above problem with periodic potential function V(x). The proof is based on a variant version of the mountain pass theorem and a Lions' type result in fractional Orlicz-Sobolev spaces.

引用

页数：22

共 37 条

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