English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this paper, we study the existence and multiplicity of homoclinicsolutions for following Hamiltonian systems with asymptotically quadraticnonlinearities at infinity \begin{eqnarray*} \ddot{u}(t)-L(t)u+\nabla W(t,u)=0.{eqnarray*} We introduce a new coercive condition and obtain a new embeddingtheorem. With this theorem, we show that above systems possess at least onenontrivial homoclinic orbits by Generalized Mountain Pass Theorem. By VariantFountain Theorem, infinitely many homoclinic orbits are obtained for aboveproblem with symmetric condition. Our asymptotically quadratic conditions aredifferent from previous ones in the references.

New homoclinic orbits for Hamiltonian systems with asymptotically quadratic growth at infinity