Geodesic
Existence of weak solutions for elliptic Dirichlet problems with variable exponent
Mathematica Bohemica, Tome 148 (2023) no. 3, pp. 283-302.

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This paper presents several sufficient conditions for the existence of weak solutions to general nonlinear elliptic problems of the type $$ \begin{cases} -{\rm div} a(x, u, \nabla u)+b(x, u, \nabla u)=0 \text {in} \ \Omega ,\\ u=0 \text {on} \ \partial \Omega , \end{cases} $$ where $\Omega $ is a bounded domain of $\mathbb R^n$, $n\ge 2$. In particular, we do not require strict monotonicity of the principal part $a(x,z,\cdot )$, while the approach is based on the variational method and results of the variable exponent function spaces.
DOI : 10.21136/MB.2022.0069-21
Classification : 35J20, 35J25, 35J70
Keywords: variable exponent; existence; variational methods; Dirichlet problem 
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Kim, Sungchol; Ri, Dukman. Existence of weak solutions for elliptic Dirichlet problems with variable exponent. Mathematica Bohemica, Tome 148 (2023) no. 3, pp. 283-302. doi : 10.21136/MB.2022.0069-21. http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0069-21/

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