Abstract
We investigate the number of periodic weak solutions for the wave equation with nonlinearity decaying at the origin. We get a theorem which shows the existence of a bounded weak solution for this problem. We obtain this result by approaching the variational method and applying the critical point theory for the indefinite functional induced from the invariant subspaces and the invariant functional.
Highlights
We investigate the number of periodic weak solutions for the wave equation with nonlinearity decaying at the origin
The purpose of this paper is to show the existence of T-periodic weak solutions of problem ( . )
For the proof of our main result, we approach the variational method and apply the critical point theory induced from the invariant subspaces and the invariant functional
Summary
And the corresponding eigenfunctions are π kt π kt sin jx sin and sin jx cos. , sin jx cos is an orthogonal base for L ( ). Sin jx cos is an orthogonal base for L ( ). L ([ , π] × R) which is T-periodic in t and equals u on. We shall denote this function by u. Let us denote an element u, in L ( ), by a u = ujk sin jx exp ik b t j> ,k with uj,k = uj,–k. H is invariant under g: Let u ∈ H such that g(u) ∈ L ( ). A u = uj,k sin jx exp ik b t, j k a b
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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.
