Existence of solutions to higher order Lane–Emden type systems

We prove existence results for the Lane–Emdentype system (−Δ)αu=|v|q(−Δ)βv=|u|p in B1⊂RN∂ru∂νr=0,r=0,…,α−1, on ∂B1∂rv∂νr=0,r=0,…,β−1, on ∂B1.where B1 is the unitary ball in RN, N>max{2α,2β}, ν is the outward pointing normal, α,β∈N, α,β≥1 and (−Δ)α=−Δ((−Δ)α−1) is the polyharmonic operator. A conti...

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Bibliographic Details
Published in:Nonlinear analysis 2018-03, Vol.168, p.130-153
Main Author: Schiera, Delia
Format: Article
Language:English
Subjects:
A priori estimates
Continuation method
Elliptic systems
Estimates
Higher order Dirichlet problems
Polyharmonic operators
Studies
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Summary:We prove existence results for the Lane–Emdentype system (−Δ)αu=|v|q(−Δ)βv=|u|p in B1⊂RN∂ru∂νr=0,r=0,…,α−1, on ∂B1∂rv∂νr=0,r=0,…,β−1, on ∂B1.where B1 is the unitary ball in RN, N>max{2α,2β}, ν is the outward pointing normal, α,β∈N, α,β≥1 and (−Δ)α=−Δ((−Δ)α−1) is the polyharmonic operator. A continuation method together with a priori estimates will be exploited. Moreover, we prove uniqueness for the particular case α=2,β=1 and p,q>1.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2017.11.011