Abstract
AbstractWe are concerned with the semi-classical states for the Choquard equation$$-{\epsilon }^2\Delta v + Vv = {\epsilon }^{-\alpha }(I_\alpha *|v|^p)|v|^{p-2}v,\quad v\in H^1({\mathbb R}^N),$$whereN⩾ 2,Iαis the Riesz potential with order α ∈ (0,N− 1) and 2 ⩽p< (N+ α)/(N− 2). When the potentialVis assumed to be bounded and bounded away from zero, we construct a family of localized bound states of higher topological type that concentrate around the local minimum points of the potentialVas ε → 0. These solutions are obtained by combining the Byeon–Wang's penalization approach and the classical symmetric mountain pass theorem.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
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.