We prove existence results for the Lane–Emdentype system (−Δ)αu=|v|q(−Δ)βv=|u|p in B1⊂RN[Formula presented]=0,r=0,…,α−1, on ∂B1[Formula presented]=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.
Existence of solutions to higher order Lane–Emden type systems
SCHIERA, DELIA
2018-01-01
Abstract
We prove existence results for the Lane–Emdentype system (−Δ)αu=|v|q(−Δ)βv=|u|p in B1⊂RN[Formula presented]=0,r=0,…,α−1, on ∂B1[Formula presented]=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.
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