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The existence of nontrivial solution for biharmonic equation with sign‐changing potential
Author(s) -
Su Yu,
Chen Haibo
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5127
Subject(s) - biharmonic equation , mathematics , sign (mathematics) , variational inequality , inequality , mathematical analysis , pure mathematics , boundary value problem
In this paper, we study the following biharmonic equation: B vΔ 2 u + V λ ( x ) u = α ( x ) f ( u ) + ν K ( x ) | u | q − 2 u inR N ,u ∈ H 2 ( R N ) ,where N ⩾5, ν ∈ (0, ν 0 ],1 < q < 2,Δ 2 u = Δ(Δ u ) and V λ ( x ) = λ a ( x ) − b ( x ) with λ > 0. Firstly, we prove the bipolar Rellich inequality. Secondly, by using bipolar Rellich inequality, Gigliardo‐Nirenberg inequality, and Ekeland variational principle, we prove the existence of nontrivial solution for problem B ν .