Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Existence Results for an Nonlinear Variable Exponents Anisotropic Elliptic Problems

  • Received : 2024.01.26
  • Accepted : 2024.06.12
  • Published : 2024.06.30
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Abstract

In this paper, we prove the existence of distributional solutions in the anisotropic Sobolev space $\mathring{W}^{1,\overrightarrow{p}(\cdot)}(\Omega)$ with variable exponents and zero boundary, for a class of variable exponents anisotropic nonlinear elliptic equations having a compound nonlinearity $G(x, u)=\sum_{i=1}^{N}(\left|f\right|+\left|u\right|)^{p_i(x)-1}$ on the right-hand side, such that f is in the variable exponents anisotropic Lebesgue space $L^{\vec{p}({\cdot})}(\Omega)$, where $\vec{p}({\cdot})=(p_1({\cdot}),{\ldots},p_N({\cdot})){\in}(C(\bar{\Omega},]1,+{\infty}[))^N$.

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Acknowledgement

The author would like to thank the referees for their comments and suggestions.

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