Abstract
We prove the existence of sign changing solutions in H 1(ℝ N ) for a stationary Schrödinger equation −Δu + a(x)u = f(x, u) with superlinear and subcritical nonlinearity f, and control the number of nodal domains. If f is odd we obtain an unbounded sequence of sign changing solutions u k , k ≥ 1, so that u k has at most k + 1 nodal domains. The bound on the number of nodal domains follows from a nonlinear version of Courant's nodal domain theorem which we also prove.
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.