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PAPER: Sign changing solutions of a semilinear equation on Heisenberg group

REF. DATE:18 June 2015 CREATED/MODIFIED: 18 January 2016 24 views No Comment

Sign changing solutions of a semilinear equation on Heisenberg group, (with J. Chen) accepted in J. Non. and Convex Anal. (2015).


ABSTRACT: This paper is concerned with the existence of multiple solutions to the semilinear equation

    \[\Delta_H\, u + |u|^{\frac{4}{Q-2}}u+\mu|\xi|^\alpha_H u=0\]

in a bounded domain of the Heisenberg group \mathbb{H}^N with Dirichlet boundary condition, where \alpha > 0 and |\xi|_H is a distance in \mathbb{H}^N. By using variational methods, we prove that this problem possesses at least one positive solution and one sign changing solution for some values of \alpha and \mu.


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Extra info: (P090/2015-06)

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