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Existence and nonexistence of nontrivial solutions for a critical biharmonic equations under the Steklov boundary conditions
  • duan tian,
  • he han,
  • lv yan
duan tian
Guangxi University

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he han
Guangxi University
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lv yan
Beijing Normal University
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In this paper, we study the existence and nonexistence of nontrivial solutions to the following critical biharmonic problem with the Steklov boundary conditions Δ2=+Δ+||2**-2 in , =Δ+=0 on , where ,, ∈ , ⊂ N( ≥ 5) is a unit ball, 2** = 2/N-4 denotes the critical Sobolev exponent for the embedding 2() →2** () and is the outer normal derivative of on . Under some assumptions on , and , we prove the existence of nontrivial solutions to the above biharmonic problem by the Mountain pass theorem and show the nonexistence of nontrivial solutions to it by the Pohozaev identity.
29 Sep 2021Submitted to Mathematical Methods in the Applied Sciences
29 Sep 2021Assigned to Editor
29 Sep 2021Submission Checks Completed
22 Oct 2021Reviewer(s) Assigned
27 Apr 2023Review(s) Completed, Editorial Evaluation Pending
28 Apr 2023Editorial Decision: Revise Minor