Eigenvalues of −Δp − Δq Under Neumann Boundary Condition
2016 ◽
Vol 59
(3)
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pp. 606-616
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Keyword(s):
Open Set
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AbstractThe eigenvalue problem −Δpu − Δqu = λ|u|q−2u with p ∊ (1,∞), q ∊ (2,∞), p ≠ q subject to the corresponding homogeneous Neumann boundary condition is investigated on a bounded open set with smooth boundary from ℝN with N ≥ 2. A careful analysis of this problem leads us to a complete description of the set of eigenvalues as being a precise interval (λ1, ∞) plus an isolated point λ = 0. This comprehensive result is strongly related to our framework, which is complementary to the well-known case p = q ≠ 2 for which a full description of the set of eigenvalues is still unavailable.
2005 ◽
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pp. 837-853
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The Schauder approach to degenerate elliptic equations with homogeneous Neumann boundary condition I
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2019 ◽
Vol 29
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