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

Journal of Partial Differential Equations ›› 2025, Vol. 38 ›› Issue (2) : 125 -141. DOI: 10.4208/jpde.v38.n2.1

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Existence and Multiplicity of Weak Solutions for a Class of Variable Exponent Elliptic Equations

Jingjing Liu ¹
, Chunshan Zhao ²^,^∗

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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

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