Abstract
We investigate the existence of nontrivial solutions and multiple solutions for the following class of elliptic equations (-?u + V(x)u = K(x)f(u), x ? RN, u ? D1,2(RN), where N ? 3, V(x) and K(x) are both unbounded potential functions and f is a function with a superquadratic growth. Firstly, we prove the existence of infinitely many solutions with compact embedding and by means of symmetric mountain pass theorem. Moreover, we prove the existence of nontrivial solutions without compact embedding in weighted Sobolev spaces and by means of mountain pass theorem. Our results extend and generalize some existing results.
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.
