Existence of solutions for p(x)-Laplacian problems on a bounded domain

By J. Chabrowski, Yongqiang Fu. 2005

193 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f477bb84ea526f141746da872d80110c11e233b5

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

On a nonhomogeneous quasilinear eigenvalue problem in sobolev spaces with variable exponent (2006, methodology): “Recent qualitative properties of solutions to quasilinear problems in Sobolev spaces with variable exponent have been obtained by Alves and Souto [2], Chabrowski and Fu [6], and Mihăilescu and Rădulescu [19].”
Overview of differential equations with non-standard growth (2010, background): “was proved in [55]: there it is assumed that B(x, u) = −λ(x)|u|p(x)−2u + b(x, u), where λ ≈ 1 and b satisfies the same conditions as B in the previously stated theorem.”
p(x)-Laplacian with indefinite weight (2011, methodology): “Recent qualitative properties of solutions to quasilinear problems in Sobolev spaces with variable exponent have been obtained by Alves and Souto [3], Chabrowski and Fu [6], and Mihăilescu and Rădulescu [17].”
Quasilinear elliptic non-homogeneous Dirichlet problems through Orlicz-Sobolev spaces (2012, background): “(12) Moreover, it follows from [20] that, sinceΦ satisfies a global∆2-condition, there exists a best positive constant λ1 such that”
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].”
Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent (2008, methodology): “For more information on properties, modelling and the application of variable exponent spaces to these fluids we refer to Acerbi and Mingione [1], Alves and Souto [3], Chabrowski and Fu [6], Diening [8], Fan et al.”
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.”
Multiple solutions for a class of p(x)-Laplacian equations in involving the critical exponent (2010, background): “1 in [3], we divide Ω into two parts: Ω1 = {x ∈ Ω : p(x) < 2}, Ω2 = {x ∈ Ω : p(x) ≥ 2}.”
Multiplicity of solutions for a class of anisotropic elliptic equations with variable exponent (2011, unknown): “For more information on properties, modelling and the application of variable exponent spaces to these fluids we refer to [16–25].”