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Solutions for a class of fractional Hamiltonian systems with exponential growth
Applicable Analysis ( IF 1.1 ) Pub Date : 2021-04-27 , DOI: 10.1080/00036811.2021.1919638
Manassés de Souza 1
Affiliation  

In this paper, we establish a weighted Trudinger–Moser type inequality and as the application of this result by using the Galerkin methods and a linking theorem, we prove the existence of weak solutions for the following class of elliptic systems: {(Δ)1/2u+V(x)u=g(x,v),v>0inR,(Δ)1/2v+V(x)v=f(x,u),u>0inR,when the potential V is neither bounded away from zero, nor bounded from above. The nonlinear terms g(x,s) and f(x,s) are superlinear at infinity and have subcritical or critical exponential growth.



中文翻译:

一类指数增长的分数哈密顿系统的解

在本文中,我们建立了一个加权的 Trudinger-Moser 型不等式,并作为该结果的应用,通过使用 Galerkin 方法和链接定理,我们证明了以下类椭圆系统的弱解的存在性:{(-Δ)1/2+(X)=G(X,v),v>0R,(-Δ)1/2v+(X)v=F(X,),>0R,当势V既不受零限制,也不受上限制。非线性项G(X,s)F(X,s)在无穷远处是超线性的并且具有亚临界或临界指数增长。

更新日期:2021-04-27
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