Über konjugierte Exponentenfolgen

Orlicz, Władysław

doi:10.4064/sm-3-1-200-211

Cited by 409 publications

(232 citation statements)

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“…Variable exponent Lebesgue spaces appeared in the literature for the first time already in a 1931 article by W. Orlicz [33]. In the years 1950 this study was carried on by Nakano [30] who made the first systematic study of spaces with variable exponent.…”

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

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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.

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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

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“…This leads us to the study of variable exponent Lebesgue and Sobolev spaces L p(x) and W k,p(x) , respectively, where p is a real-valued function. Spaces of variable exponent can be traced back to Orlicz [5], but the current investigation goes back to a paper Kováčik and Rákosník [3]. The basic properties of these spaces can be found in the paper [3]; many of these properties were independently established by Fan and Zhao [4].…”

Section: Introductionmentioning

confidence: 99%

A UNIFORM ABSOLUTE CONTINUITY OF INTEGRAL RESULT IN $L^{p\left(x\right)}$

Kaya¹

2017

Int. J. of Appl. Math.

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“…Solutions of these problems belong to some generalized Lebesgue and Sobolev spaces. The spaces were first introduced in [16]. The properties of these spaces and their applications to nonlinear differential equations with variable exponents of nonlinearity have been actively studied (see, e.g., [17][18][19][20][21][22][23][24]).…”

Section: Bu(t) ) + A(t; U(t))mentioning

confidence: 99%