Home » Pub-Topic: Partial Differential Equations, Pub-Type: Proceedings with Referee

PAPER: Two nontrivial solutions of a class of elliptic equations with singular term

REF. DATE:22 September 2011 CREATED/MODIFIED: 14 January 2016 172 views No Comment

Two nontrivial solutions of a class of elliptic equations with singular term (with J. Chen, K. Murillo), Dynamical Systems and Differential Equations, DCDS Supplement 2011. Proceedings of the 8th AIMS International Conference, Wei Feng et al., 272-281, Dresden (Germany), 2011. ISBN: 978-1-60133-007-9


ABSTRACT: We consider the existence of nontrivial solutions of the equation

    \[-\Delta u -{\frac{\lambda }{{|x|^{2}}}}u= |u|^{2^{\ast}-2}u  + \mu|x|^{\alpha-2}u + f(x)|u|^{\gamma},\quad x\in \Omega\backslash\{0\},\:\:\: u\in H^1_0(\Omega),\]

where 0\in\Omega is a smooth bounded domain in \mathbb{R}^N (N\geq 3). By variational methods and Nehari set techniques, we show that this equation has at least two nontrivial solutions in H^1_0(\Omega), under some additional hypotheses on \lambda>0, \mu>0, \alpha>0, 0\leq\gamma<1 and f\in L^\infty(\Omega), which may be sign-changing. If f>0 then the solutions are positive.


Download: Preprint version (RIA |  download) / Publisher version (Discrete Contin. Dyn. Syst.)
Extra info: (P100/2011-09) (free/open access)

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