Orlicz Spaces and Modular Spaces

Musielak, Julian

doi:10.1007/bfb0072210

Cited by 1,459 publications

(1,120 citation statements)

References 0 publications

Supporting

Mentioning

1,112

Contrasting

Unclassified

Order By: Relevance

“…In the years 1950 this study was carried on by Nakano [30] who made the first systematic study of spaces with variable exponent. Later, the Polish mathematicians investigated the modular function spaces (see, e.g., the basic monograph Musielak [29]). Variable exponent Lebesgue spaces on the real line have been independently developed by Russian researchers.…”

Section: Introduction and Auxiliary Resultsmentioning

confidence: 99%

Entire solutions of multivalued nonlinear Schrödinger equations in Sobolev spaces with variable exponent

Dinu¹

2006

Nonlinear Analysis: Theory, Methods & Applications

View full text Add to dashboard Cite

Abstract. We establish the existence of an entire solution for a class of stationary Schrödinger equations with subcritical discontinuous nonlinearity and lower bounded potential that blows-up at infinity. The abstract framework is related to Lebesgue-Sobolev spaces with variable exponent. The proof is based on the critical point theory in the sense of Clarke and we apply Chang's version of the Mountain Pass Lemma without the PalaisSmale condition for locally Lipschitz functionals. Our result generalizes in a nonsmooth framework a result of Rabinowitz [35] on the existence of ground-state solutions of the nonlinear Schrödinger equation.

show abstract

Section: Introduction and Auxiliary Resultsmentioning

confidence: 99%

Entire solutions of multivalued nonlinear Schrödinger equations in Sobolev spaces with variable exponent

Dinu¹

2006

Nonlinear Analysis: Theory, Methods & Applications

View full text Add to dashboard Cite

show abstract

“…Define the Lebesgue space with a variable exponent p(·), which is the so-called Nakano space and a special sort of Musielak-Orlicz spaces (see [32]), as follows: …”

Section: Preliminariesmentioning

confidence: 99%

Nonlinear diffusion equations driven by the p(·)-Laplacian

Akagi

Matsuura

2012

Nonlinear Differ. Equ. Appl.

View full text Add to dashboard Cite

Abstract. This paper is concerned with nonlinear diffusion equations driven by the p(·)-Laplacian with variable exponents in space. The wellposedness is first checked for measurable exponents by setting up a subdifferential approach. The main purposes are to investigate the large-time behavior of solutions as well as to reveal the limiting behavior of solutions as p(·) diverges to the infinity in the whole or in a subset of the domain. To this end, the recent developments in the studies of variable exponent Lebesgue and Sobolev spaces are exploited, and moreover, the spatial inhomogeneity of variable exponents p(·) is appropriately controlled to obtain each result. Mathematics Subject Classification (2010). Primary 35K92; Secondary 35K55, 46E35.

show abstract

“…A sequence M = (Mi) of Orlicz functions is called a Musielak-Orlicz function (see [14]). We associate with this function two sequences (e* y h.M we denote the subspace of IM which is defined to be the closure in IM of the space of all sequences in 1° with finite number of coordinates different from 0 (the closure is taken in the norm topology).…”

Section: Introductionmentioning

confidence: 99%

“…The spaces IM and HM are Banach spaces under either of these two norms (see [1,11,14]). In [11] these spaces are called modular sequence spaces.…”

Section: Introductionmentioning

confidence: 99%

Smooth, very smooth and strongly smooth points in Musielak-Orlicz sequence spaces

Bian

Hudzik

Wang

2001

Bull. Austral. Math. Soc.

View full text Add to dashboard Cite

show abstract

Orlicz Spaces and Modular Spaces

Cited by 1,459 publications

References 0 publications

Entire solutions of multivalued nonlinear Schrödinger equations in Sobolev spaces with variable exponent

Entire solutions of multivalued nonlinear Schrödinger equations in Sobolev spaces with variable exponent

Nonlinear diffusion equations driven by the p(·)-Laplacian

Smooth, very smooth and strongly smooth points in Musielak-Orlicz sequence spaces

Contact Info

Product

Resources

About