Abstract
This paper deals with the existence of sign-changing solutions for the fourth-order nonlinear boundary value problem u ( 4 ) = f ( u , u ″ ) , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 , where f : R 2 → R is a continuously odd function. Some conditions on f guaranteeing the existence and multiplicity of sign-changing solutions are presented. The existence and multiplicity conditions concern the eigenline of the associated two-parameter linear eigenvalue problem. The discussion is based on the fixed point index theory in cones and an anti-symmetrical extension method of solution.
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.
