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August 2020 Multiple solutions for generalized biharmonic equations with singular potential and two parameters
Ruiting Jiang, Chengbo Zhai
Rocky Mountain J. Math. 50(4): 1355-1368 (August 2020). DOI: 10.1216/rmj.2020.50.1355

Abstract

We investigate a more general nonlinear biharmonic equation

Δ 2 u β Δ p u + V λ ( x ) u = f ( x , u )  in  N ,

where Δ2:=Δ(Δ) is the biharmonic operator, N1, λ>0 and β are parameters, Δpu= div(|u|p2u) with p2. Differently from previous works on biharmonic problems, we replace Laplacian with p-Laplacian, and suppose that V(x)=λa(x)b(x) with λ>0 and b(x) can be singular at the origin, in particular we allow β to be a real number. Under suitable conditions on Vλ(x) and f(x,u), the multiplicity of solutions is obtained for λ>0 sufficiently large. Our analysis is based on variational methods as well as the Gagliardo–Nirenberg inequality.

Citation

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Ruiting Jiang. Chengbo Zhai. "Multiple solutions for generalized biharmonic equations with singular potential and two parameters." Rocky Mountain J. Math. 50 (4) 1355 - 1368, August 2020. https://doi.org/10.1216/rmj.2020.50.1355

Information

Received: 28 February 2019; Revised: 6 October 2019; Accepted: 31 October 2019; Published: August 2020
First available in Project Euclid: 29 September 2020

zbMATH: 07261868
MathSciNet: MR4154811
Digital Object Identifier: 10.1216/rmj.2020.50.1355

Subjects:
Primary: 35B38, 35J35, 35J92

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 4 • August 2020
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