Multiple solutions for a class of double phase problem without the Ambrosetti–Rabinowitz conditions
作者： Bin Ge , De-Jing Lv , Jian-Fang Lu
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摘要: Abstract In the present paper, in view of variational approach, we consider existence and multiplicity weak solutions for a class double phase problem − div ( | ∇ u p 2 + x ) q = λ f , Ω 0 on ∂ where N ≥ 1 . Firstly, by Fountain Dual Theorem with Cerami condition, obtain some infinitely many above under weaker assumptions Secondly, prove that this has at least one nontrivial solution any parameter > small enough, also blows up, Sobolev norm, as → Finally, imposing additional establish using Krasnoselskii’s genus theory equation.
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