带有奇异p-Laplacians算子的分数阶差分方程边值问题解的存在性  

Existence of solution for boundary value problem of fractional order difference equation with singular pLaplacians operator

作　　者：金元峰[1] 宋健楠[1] 李霄 侯成敏[1] 

机构地区：[1]延边大学理学院,吉林延吉133002

出　　处：《东北石油大学学报》2017年第4期116-122,共7页Journal of Northeast Petroleum University

基　　金：国家自然科学基金项目(11161049;11361066)

摘　　要：考虑离散分数阶边值问题{Δ_(ν+a)~ν(t^(N-1)φ(b▽~νu(t)))+t^(N-1)[λ|u(t)|m^(-2) u(t)-f(t,u(t))]=0,t∈[a,b]N_a;[b▽~νu(t)]_t=b+ν=[b▽~νu(t)]t=a+ν-1=0。其中ν∈(0,1),a,b∈Z,0≤a<b-1,N∈Z^+,N≥1,φ∶=Φ′∶(-d,d)→R满足φ(t)=0,t∈R\[-d,d]∪{0}。Φ∶[-d,d]→R在[-d,d]连续,在(-d,d)内可导。λ>0,m≥2为固定实数。f(·,u)∶[-d,d]N-d×R→R是关于第二个变量的连续函数且满足Ambrosetti-Rabinorwitz条件。建立变分框架,利用临界点定理,得到离散分数阶边值问题解的存在性结果。We consider the discrete fractional order boundary value problem {Δ_(ν+a)~ν(t^(N-1)φ(b▽~νu(t)))+t^(N-1)[λ|u(t)|m^(-2) u(t)-f(t,u(t))]=0,t∈[a,b]N_a;[b▽~νu(t)]_t=b+ν=[b▽~νu(t)]t=a+ν-1=0。Where ν∈(0,1),a,b∈Z,0≤a<b-1,N∈Z+,N≥1,φ∶=Φ′∶(-d,d)→Rsatisfyφ(t)=0,t∈R\[-d,d]∪{0}。Φ∶[-d,d]→Ris continuous on interval[-d,d]and it is derivable in interval(-d,d).λ>0,m≥2are fix real numbers.f(·,u)∶[-d,d]N-d×R→Ris continuous about second variables and satisfies Ambrosatti-Rabinorwitz condition.By establishing variational framework and using critical point theorem,the existence result of solution is obtained.

关 键 词：分数阶差分方程 边值问题 临界点定理 存在性 

分 类 号：O175.7[理学—数学]