Home » Pub-Topic: Partial Differential Equations, Pub-Type: Articles in International Journals

PAPER: Positive and sign-changing solutions of a Schrödinger-Poisson system involving a critical nonlinearity

REF. DATE:4 June 2013 CREATED/MODIFIED: 15 January 2016 224 views No Comment

Positive and sign-changing solutions of a Schrödinger-Poisson system involving a critical nonlinearity (with L. Huang, J. Chen), J. Math. Anal. Appl. 408:1(2013), 55–69.


ABSTRACT: We consider the Schrödinger-Poisson system

    \[\left\{\begin{array}{ll}        -\Delta u +u +l(x)\phi u = k(x)|u|^4u +\mu h(x)u  \quad & \ \hbox{in} \ {\bkR}^3,\\ -\Delta \phi = l(x)u^2\quad & \ \hbox{in} \ {\bkR}^3, \end{array}\right.\]

where \mu is a positive constant and the nonlinear growth of |u|^4u reaches the Sobolev critical exponent, since 2^*=6 for three spatial dimensions. We prove the existence of (at least) a pair of fixed sign and a pair of sign-changing solutions in H^1({\bkR}^3)\times D^{1, 2}({\bkR}^3) under some suitable conditions on the non-negative functions l, k, h, but not requiring any symmetry property on them.


Download: Preprint version (RIA |  download) / Publisher version (doi:10.1016/j.jmaa.2013.05.071)
Extra info: (P082/2013-06-04)

Leave your response!

You must be logged in to post a comment.