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December 2020 Three positive solutions of fourth-order problems with clamped beam boundary conditions
Dongliang Yan
Rocky Mountain J. Math. 50(6): 2235-2244 (December 2020). DOI: 10.1216/rmj.2020.50.2235

Abstract

We investigate the existence of three positive solutions of fourth order problems with clamped beam boundary conditions

u ( x ) = λ f ( u ( x ) ) , x ( 1 , 1 ) , u ( 1 ) = u ( 1 ) = u ( 1 ) = u ( 1 ) = 0 ,

where λ>0 is a parameter, fC[0,) is nondecreasing, f(0)=0, f(s)>0 for all s>0. Especially, we obtain an S-shaped unbounded connected component in the symmetric positive solutions set. The proof is based on the directions of a bifurcation.

Citation

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Dongliang Yan. "Three positive solutions of fourth-order problems with clamped beam boundary conditions." Rocky Mountain J. Math. 50 (6) 2235 - 2244, December 2020. https://doi.org/10.1216/rmj.2020.50.2235

Information

Received: 3 March 2020; Revised: 13 March 2020; Accepted: 29 May 2020; Published: December 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/rmj.2020.50.2235

Subjects:
Primary: 34B05, 34C23, 74K10

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 6 • December 2020
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