The Nehari Manifold for p-Laplacian Equation with Dirichlet Boundary Condition
2007 ◽
Vol 12
(2)
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pp. 143-155
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Keyword(s):
The Nehari manifold for the equation −∆pu(x) = λu(x)|u(x)|p−2 + b(x)|u(x)|γ−2u(x) for x ∈ Ω together with Dirichlet boundary condition is investigated in the case where 0 < γ < p. Exploiting the relationship between the Nehari manifold and fibrering maps (i.e., maps of the form of t → J(tu) where J is the Euler functional associated with the equation), we discuss how the Nehari manifold changes as λ changes, and show how existence results for positive solutions of the equation are linked to the properties of Nehari manifold.
2014 ◽
Vol 16
(04)
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pp. 1350048
2016 ◽
Vol 2016
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pp. 1-10
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2020 ◽
Vol 11
(1)
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pp. 1
2006 ◽
Vol 49
(3)
◽
pp. 709-734
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2010 ◽
Vol 248
(5)
◽
pp. 1175-1211
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2015 ◽
Vol 17
(03)
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pp. 1450011
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