Abstract
We discuss existence and multiplicity of solutions of the periodic problem for the curvature-like equation − ( u ′ / a 2 + u ′ 2 ) ′ = f ( t , u ) by means of variational techniques in the space of bounded variation functions. As a = 0 is allowed, both the prescribed curvature equation and the 1-Laplace equation are considered. We are concerned with the case where the right-hand side f of the equation interacts with the beginning of the spectrum of the 1-Laplace operator with periodic boundary conditions on [ 0 , T ] , being mainly interested in the situation where ess sup [ 0 , T ] × R f ( t , s ) may differ from − ess inf [ 0 , T ] × R f ( t , s ) .
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.
