Results 51 to 58 of about 152 (58)

Finding critical points whose polarization is also a critical point [PDF]

open access: yesTopol. Methods Nonlinear Anal. 40 (2012), no. 2, 371-379, 2011
We show that near any given minimizing sequence of paths for the mountain pass lemma, there exists a critical point whose polarization is also a critical point. This is motivated by the fact that if any polarization of a critical point is also a critical point and the Euler-Lagrange equation is a second-order semi-linear elliptic problem, T. Bartsch, T.
arxiv  

Bifurcation and multiplicity results for critical fractional p-Laplacian problems [PDF]

open access: yesarXiv, 2014
In this paper we investivate bifurcation results for a class of problem in a smooth bounded domain involving the fractional p-Laplacian operator and with a nonlinearity that reaches the critical growth with respect to the fractional Sobolev embedding.
arxiv  

Two characterizations of quasiconvexity [PDF]

open access: yesarXiv
We present two characterizations of quasiconvexity for radially semicontinuous mappings defined on a convex subset of a real linear space. As an application we obtain an extension of the Sion's minimax theorem, as well as a new characterization of quasiconvex risk measures.
arxiv  

Compactness of Palais-Smale sequences with controlled Morse Index for a Liouville type functional [PDF]

open access: yesarXiv
We prove that Palais-Smale sequences for Liouville type functionals on closed surfaces are precompact whenever they satisfy a bound on their Morse index. As a byproduct, we obtain a new proof of existence of solutions for Liouville type mean-field equations in a supercritical regime.
arxiv  

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