Complex Anal. Oper. Theory Complex Analysis https://doi.org/10.1007/s11785-018-0809-2 and Operator Theory A singular System Involving the Fractional p-Laplacian Operator via the Nehari Manifold Approach Kamel Saoudi Received: 24 December 2017 / Accepted: 28 May 2018 © Springer International Publishing AG, part of Springer Nature 2018 Abstract In this work we study the fractional p-Laplacian equation with singular nonlinearity s q−2 1−α −α 1−β ⎪ (−) u = λa(x )|u| u + c(x )|u| |v| , in , ⎪ p 2−α−β 1−β s q−2 1−α −β (−) v = μb(x )|v| v + c(x )|u| |v| , in , 2−α−β u = v = 0, in R \, ∗ ∗ N where 0 <α < 1, 0 <β < 1, 2−α −β< p < q < p , p = is the fractional s s N − ps Sobolev exponent, λ, μ are two parameters, a, b, c ∈ C () are non-negative weight functions with compact support in , and (−) is the fractional p-Laplace operator. We use the Nehari manifold approach and some variational techniques in order to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ and μ. Keywords
Complex Analysis and Operator Theory – Springer Journals
Published: Jun 4, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera