Displaying similar documents to “Some results on critical groups for a class of functionals defined on Sobolev Banach spaces”

A min-max theorem for multiple integrals of the Calculus of Variations and applications

David Arcoya, Lucio Boccardo (1995)

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

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In this paper we deal with the existence of critical points for functionals defined on the Sobolev space W 0 1 , 2 ⁢ Ω by J ⁢ v = ∫ Ω I ⁢ x , v , D ⁢ v ⁢ d ⁢ x , v ∈ W 0 1 , 2 ⁢ Ω , where Ω is a bounded, open subset of R N . Since the differentiability can fail even for very simple examples of functionals defined through multiple integrals of Calculus of Variations, we give a suitable version of the Ambrosetti-Rabinowitz Mountain Pass Theorem, which enables us to the study of critical points for functionals which are not differentiable in all directions....

On a class of nonlocal problem involving a critical exponent

Anass Ourraoui (2015)

Communications in Mathematics

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In this work, by using the Mountain Pass Theorem, we give a result on the existence of solutions concerning a class of nonlocal p -Laplacian Dirichlet problems with a critical nonlinearity and small perturbation.