کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4614562 | 1339293 | 2016 | 28 صفحه PDF | دانلود رایگان |
In this paper, we investigate a nonlocal and nonlinear elliptic problem,equation(P){−a(∫Ω|∇u|2dx)Δu=λu+up in Ω,u=0 on ∂Ω, where N≤3N≤3, Ω⊂RNΩ⊂RN is a bounded domain with smooth boundary ∂Ω, a is a nondegenerate continuous function, p>1p>1 and λ∈Rλ∈R. We show several effects of the nonlocal coefficient a on the structure of the solution set of (P). We first introduce a scaling observation and describe the solution set by using that of an associated semilinear problem. This allows us to get unbounded continua of solutions (λ,u)(λ,u) of (P). A rich variety of new bifurcation and multiplicity results are observed. We also prove that the nonlocal coefficient can induce up to uncountably many solutions in a convenient way. Lastly, we give some remarks from the variational point of view.
Journal: Journal of Mathematical Analysis and Applications - Volume 435, Issue 2, 15 March 2016, Pages 1710–1737