Abstract
In this paper, we study the existence and nonexistence of multiple positive solutions for the inhomogeneous Neumann boundary value problem (∗) Δu+u p−λu=0, with D γu=ϕ(x), under some assumptions on the boundary ∂Ω and the function ϕ( x). For ϕ( x)⩾0, ϕ( x)≢0, ϕ(x)∈C α( Ω ̄ ) , it is shown that there exists a constant λ ∗>0 such that problem ( ∗) possesses at least two positive solutions if λ∈(λ ∗,∞) and at least one positive solution if λ=λ ∗ . Furthermore, there are no positive solutions for problem ( ∗) if λ∈(−∞,λ ∗) .
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
