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Indices of Orlicz spaces and some applications

Alberto Fiorenza, Miroslav Krbec (1997)

Commentationes Mathematicae Universitatis Carolinae

We study connections between the Boyd indices in Orlicz spaces and the growth conditions frequently met in various applications, for instance, in the regularity theory of variational integrals with non-standard growth. We develop a truncation method for computation of the indices and we also give characterizations of them in terms of the growth exponents and of the Jensen means. Applications concern variational integrals and extrapolation of integral operators.

Infinitely many solutions for Kirchhoff-type equations involving critical growth in Orlicz-Sobolev with negative energies

Elmostafa Bendib, Mustapha Khiddi (2025)

Applications of Mathematics

We investigate a class of Kirchhoff-type equations characterized by critical growth within Orlicz-Sobolev spaces. The main result establishes the existence of infinitely many solutions with negative energy. Using an adapted concentration-compactness principle and advanced variational methods, we overcome key challenges such as non-compactness and non-differentiability to the associated functionals. This work extends existing results to more general functional spaces, offering new insights into nonlocal...

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