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Volume 38, Issue 2
Existence and Multiplicity of Weak Solutions for a Class of Variable Exponent Elliptic Equations

Jingjing Liu & Chunshan Zhao

DOI: 10.4208/jpde.v38.n2.1

J. Part. Diff. Eq., 38 (2025), pp. 125-141.

Published online: 2025-06

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  • Abstract

In this paper we will study the existence of one, two and three weak solutions for a class of variable exponent elliptic equations under appropriate growth conditions on the nonlinearity. Our technical approach is based on the existence theorems obtained by G. Bonanno.

  • Keywords

Weak solutions, $p(x)$-Laplacian, weighted variable exponent Sobolev spaces.

  • AMS Subject Headings

35D30, 35J70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-38-125, author = {Liu , Jingjing and Zhao , Chunshan}, title = {Existence and Multiplicity of Weak Solutions for a Class of Variable Exponent Elliptic Equations}, journal = {Journal of Partial Differential Equations}, year = {2025}, volume = {38}, number = {2}, pages = {125--141}, abstract = {

In this paper we will study the existence of one, two and three weak solutions for a class of variable exponent elliptic equations under appropriate growth conditions on the nonlinearity. Our technical approach is based on the existence theorems obtained by G. Bonanno.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v38.n2.1}, url = {http://global-sci.org/intro/article_detail/jpde/24212.html} }
TY - JOUR T1 - Existence and Multiplicity of Weak Solutions for a Class of Variable Exponent Elliptic Equations AU - Liu , Jingjing AU - Zhao , Chunshan JO - Journal of Partial Differential Equations VL - 2 SP - 125 EP - 141 PY - 2025 DA - 2025/06 SN - 38 DO - http://doi.org/10.4208/jpde.v38.n2.1 UR - https://global-sci.org/intro/article_detail/jpde/24212.html KW - Weak solutions, $p(x)$-Laplacian, weighted variable exponent Sobolev spaces. AB -

In this paper we will study the existence of one, two and three weak solutions for a class of variable exponent elliptic equations under appropriate growth conditions on the nonlinearity. Our technical approach is based on the existence theorems obtained by G. Bonanno.

Liu , Jingjing and Zhao , Chunshan. (2025). Existence and Multiplicity of Weak Solutions for a Class of Variable Exponent Elliptic Equations. Journal of Partial Differential Equations. 38 (2). 125-141. doi:10.4208/jpde.v38.n2.1
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