A survey on existence of a solution to fractional difference boundary value problem with |u|^{p-۲}u term
عنوان مقاله: A survey on existence of a solution to fractional difference boundary value problem with |u|^{p-۲}u term
شناسه ملی مقاله: JR_MACO-4-1_004
منتشر شده در در سال 1402
شناسه ملی مقاله: JR_MACO-4-1_004
منتشر شده در در سال 1402
مشخصات نویسندگان مقاله:
Mohsen Khaleghi Moghadam - Department of Basic Sciences
خلاصه مقاله:
Mohsen Khaleghi Moghadam - Department of Basic Sciences
In this paper, we deal with the existence of a non-trivial
solution for the following fractional discrete boundary-value problem for any k in [۱,T]_{mathbb{N}_{۰}}
begin{equation*}
begin{cases}
_{T+۱}nabla_k^{alpha}left( ^{}_knabla_{۰}^{alpha}(u(k))right)+{^{}_knabla}_{۰}^{alpha}left( ^{}_{T+۱}nabla_k^{alpha}(u(k))right)+phi_{p}(u(k))=lambda f(k,u(k)),
u(۰)= u(T+۱)=۰,
end{cases}
end{equation*}
where ۰< alpha<۱ and ^{}_knabla_{۰}^{alpha} is the left nabla discrete fractional difference and ^{}_{T+۱}nabla_k^{alpha} is the right nabla discrete fractional difference f: [۱,T]_{mathbb{N}_{۰}}timesmathbb{R}tomathbb{R} is
a continuous function, lambda>۰ is a parameter and phi _{p} is the so called p-Laplacian
operator defined as phi _{p}(s)=|s|^{p-۲}s and ۱
کلمات کلیدی: Discrete fractional calculus, Discrete nonlinear boundary value problem, Non trivial solution, Variational methods, Critical point theory.
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1900574/