Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis

By Vicentiu D. Rădulescu, Dušan D. Repovš. 2015

512 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5cea57bfb30c10e0e9a63a1a0c59d047cdc60c6c

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Citations in the corpus

New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, unknown): “R˘adulescu-Repovš–Zhang [67] (double phase anisotropic variational problems with variable exponents), Zeng–Bai–Gasi´nski– Winkert [71] (implicit obstacle double phase problems), Zeng–”
Lipschitz Bounds and Nonautonomous Integrals (2020, background): “Connections to related function spaces have been studied too [27, 49, 63].”
Basic results of fractional Orlicz-Sobolev space and applications to non-local problems (2019, methodology): “We refer the reader to [15, 16, 30, 31, 37] for more details on Sobolev space with variable exponent.”
Existence and multiplicity results for a newp(x)-Kirchhoff problem (2019, background): “Some important and interesting results can be found, for example, in [4, 5, 3, 2, 7, 10, 8, 11, 12, 13, 15, 18, 21, 19, 22, 23, 24, 25, 29, 30, 31, 32, 33, 40] and references therein.”
Double phase problems with variable growth (2018, methodology): “4) are essentially due to Fan and Zhao [29], see also [21], [22], and [30].”
Existence Results for Double Phase Problem in Sobolev–Orlicz Spaces with Variable Exponents in Complete Manifold (2021, background): “2 Mathematical background and auxiliary results In this section, we recall the most important and relevant properties and notations about Sobolev spaces with variable exponents and Sobolev spaces with variable exponents on manifolds, and we prove some properties, that we will need in our analysis of”
On the removability of isolated singular points for elliptic equations involving variable exponent (2015, background): “Since Kováčik and Rákosník first studied the Lp(x) spaces andWk,p(x) spaces in [12], many results have been obtained concerning these kinds of variable exponent spaces, see examples in [4, 7, 8, 10, 11, 16, 17, 21].”
Multiplicity results for the non-homogeneous fractional p-Kirchhoff equations with concave–convex nonlinearities (2015, background): “For its applications to partial differential equations with variable exponents, for example, we refer to [51].”
A multiplicity result for asymptotically linear Kirchhoff equations (2017, background): “2), we refer the readers to [1, 2, 5, 24] and the references therein.”
Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves (2019, methodology): “For general properties of function spaces with variable exponent we refer to [33].”
On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent (2017, methodology): “We refer to [11, 19] and the references therein.”