Abstract
In this paper, we study the fourth order elliptic equations Δ2u−Δu+λV(x)u=f(x,u) in RN, u∈H2(RN), where λ≥1 and the nonlinearity f is either superlinear or sublinear at infinity. We establish the existence and multiplicity results without the compactness of embedding of the working space, which unify and sharply improve the recent results of Liu, Chen and Wu [J. Liu, S. Chen, X. Wu, Existence and multiplicity of solutions for a class of fourth-order elliptic equations in RN, J. Math. Anal. Appl. 395 (2012) 608–615].
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.
