Jaeyoung Byeon, Louis Jeanjean, Mihai Mariş
Published 2008-06-02Version 1
We give a simple proof of the fact that for a large class of quasilinear elliptic equations and systems the solutions that minimize the corresponding energy in the set of all solutions are radially symmetric. We require just continuous nonlinearities and no cooperative conditions for systems. Thus, in particular, our results cannot be obtained by using the moving planes method. In the case of scalar equations, we also prove that any least energy solution has a constant sign and is monotone with respect to the radial variable.
On the symmetry of minimizers
Positive least energy solutions for $k$-coupled Schrödinger system with critical exponent: the higher dimension and cooperative case
On the behavior of least energy solutions of a fractional $(p,q(p))$-Laplacian problem as p goes to infinity
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