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Some results on critical groups for a class of functionals defined on Sobolev Banach spaces

Silvia Cingolani, Giuseppina Vannella (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We present critical groups estimates for a functional f defined on the Banach space W 0 1 , p Ω , Ω bounded domain in R N , 2 < p < , associated to a quasilinear elliptic equation involving p -laplacian. In spite of the lack of an Hilbert structure and of Fredholm property of the second order differential of f in each critical point, we compute the critical groups of f in each isolated critical point via Morse index.

Speculating About Mountains

Ribarska, N., Tsachev, Ts., Krastanov, M. (1996)

Serdica Mathematical Journal

∗Partially supported by Grant MM 409/94 of the Mininstry of Education, Science and Technology, Bulgaria. ∗∗Partially supported by Grants MM 521/95, MM 442/94 of the Mininstry of Education, Science and Technology, Bulgaria.The definition of the weak slope of continuous functions introduced by Degiovanni and Marzocchi (cf. [8]) and its interrelation with the notion “steepness” of locally Lipschitz functions are discussed. A deformation lemma and a mountain pass theorem for usco mappings are proved....

Stabilities of F-Yang-Mills fields on submanifolds

Gao-Yang Jia, Zhen Rong Zhou (2013)

Archivum Mathematicum

In this paper, we define an F -Yang-Mills functional, and hence F -Yang-Mills fields. The first and the second variational formulas are calculated, and the stabilities of F -Yang-Mills fields on some submanifolds of the Euclidean spaces and the spheres are investigated, and hence the theories of Yang-Mills fields are generalized in this paper.

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