Geodesic
Existence of weak solutions for elliptic Dirichlet problems with variable exponent
Mathematica Bohemica, Tome 148 (2023) no. 3, pp. 283-302 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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

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