Abstract
In this paper, we study the existence and multiplicity of solutions to the fourth-order boundary value problem u ( 4 ) ( t ) + β u ″ ( t ) − α u ( t ) = f ( t , u ( t ) ) for all t ∈ [ 0 , 1 ] subject to Dirichlet boundary value condition, where f ∈ C 1 ( [ 0 , 1 ] × R 1 , R 1 ) , α , β ∈ R 1 . By using the critical point theory and the infinite dimensional Morse theory, we establish some conditions on f which are able to guarantee that this boundary value problem has at least one nontrivial, two nontrivial, m distinct pairs of solutions, and infinitely many solutions, respectively. Our results improve some recent works.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
