Lebesgue and Sobolev Spaces with Variable Exponents

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Multiple solutions for a p(x)-Kirchhoff-type equation with sign-changing nonlinearities (2013, neutral): “provided jujp(x)5 1 and jun ujpðxÞ ! 0 , pðxÞðun uÞ ! 0: ð1:7Þ In this article, we assume that p2C þ ð Þ, where C þ ð Þ is the space of all the functions of Cþð Þ which are logarithmic Hölder continuous, that is, there exists R4 0 such that for all x, y2 with 05 jx yj 12, j pðxÞ pð yÞj R logjx yj, s”
Double phase problems with variable growth (2018, methodology): “4) are essentially due to Fan and Zhao [29], see also [21], [22], and [30].”
Nonlinear elliptic equations with variable exponent: Old and new (2015, methodology): “We refer to themonograph by Diening, Harjulehto, Hästö, and Ruzicka [10] for a comprehensive introduction to”
Commutators of multilinear Calderón-Zygmund operators with kernels of Dini's type and applications (2019, neutral): “The following generalized Hölder’s inequality holds (see [3] or [7]).”
Regularity of solutions to a class of variable–exponent fully nonlinear elliptic equations (2018, methodology): “In addition, the θ(x)-growth regime suggests the use of Lebesgue and Sobolev spaces with variable exponents; see [22].”
Monotone operator theory for unsteady problems in variable exponent spaces (2012, methodology): “We have the following result which can be found in [28,30] for the case of constant exponents and in [14] for variable exponents.”