EXISTENCE OF THREE SOLUTIONS FOR A DOUBLY EIGENVALUE FOURTH-ORDER BOUNDARY VALUE PROBLEM

In this paper we consider the existence of at least three solutions for the Dirichlet problem { u i v + α u ″ + β u = λ f ( x , u ) + μ g ( x , u ) , x ∈ ( 0 , 1 ) u ( 0 ) = u ( 1 ) = 0 , u ″ ( 0 ) = u ″ ( 1 ) = 0 , whereα, βare real constants,f, g: [0, 1] ×R→RareL 2-Carathéodory functions and λ,μ&g...

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Published inTaiwanese journal of mathematics Vol. 15; no. 1; pp. 201 - 210
Main Authors Afrouzi, G. A., Heidarkhani, S., O'Regan, Donal
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.02.2011
Subjects
Boundary value problems
Mathematical functions
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ISSN1027-5487
2224-6851
DOI10.11650/twjm/1500406170

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Summary:In this paper we consider the existence of at least three solutions for the Dirichlet problem { u i v + α u ″ + β u = λ f ( x , u ) + μ g ( x , u ) , x ∈ ( 0 , 1 ) u ( 0 ) = u ( 1 ) = 0 , u ″ ( 0 ) = u ″ ( 1 ) = 0 , whereα, βare real constants,f, g: [0, 1] ×R→RareL 2-Carathéodory functions and λ,μ> 0. The approach is based on variational methods and critical points. 2000Mathematics Subject Classification: 34B15. Key words and phrases: Fourth-order equations, Three solutions, Critical point, Multiplicity results.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500406170