Abstract
ABSTRACTIn this paper, we are concerned with the multiplicity and concentration of solutions for a Hamiltonian system driven by the fractional Laplace operator with variable order derivative. More precisely, we consider where , , is a nonlocal fractional integro-differential operator with variable order derivative, is a parameter, is a real symmetric matrix and belongs to . Under some suitable assumptions, we show that the system admits at least two distinct homoclinic solutions. Moreover, we investigate the concentration of solutions as . This paper is the first time to deal with Hamiltonian systems with variable order fractional derivatives. Moreover, our system is anisotropic. Thus this is different from other papers in the literature.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.