Abstract
We are concerned with the semi-linear Schrodinger equation: - Δ u + V ( x ) u = K ( x ) | u | 2 * - 2 u + g ( x , u ) u ∈ H 1 ( R N ) where N ⩾ 3 , V ( x ) is a continuous function such that the spectrum σ ( - Δ + V ( x ) ) of - Δ + V ( x ) in L 2 ( R N ) has a negative part, 2 * = 2 N / ( N - 2 ) is the critical Sobolev exponent, K ( x ) is a bounded positive function, g is of subcritical growth. We prove that under suitable hypotheses the equation has a nontrivial solution.
Sign-in/Register to access full text options 
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.
