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Existence of radial solutions for a p ( x ) $p(x)$ -Laplacian Dirichlet problem
Advances in Difference Equations ( IF 3.1 ) Pub Date : 2021-04-21 , DOI: 10.1186/s13662-021-03369-x Maria Alessandra Ragusa , Abdolrahman Razani , Farzaneh Safari
中文翻译:
ap(x)$ p(x)$ -Laplacian Dirichlet问题的径向解的存在性
更新日期:2021-04-21
Advances in Difference Equations ( IF 3.1 ) Pub Date : 2021-04-21 , DOI: 10.1186/s13662-021-03369-x Maria Alessandra Ragusa , Abdolrahman Razani , Farzaneh Safari
In this paper, using variational methods, we prove the existence of at least one positive radial solution for the generalized \(p(x)\)-Laplacian problem
$$ -\Delta _{p(x)} u + R(x) u^{p(x)-2}u=a (x) \vert u \vert ^{q(x)-2} u- b(x) \vert u \vert ^{r(x)-2} u $$with Dirichlet boundary condition in the unit ball in \(\mathbb{R}^{N}\) (for \(N \geq 3\)), where a, b, R are radial functions.
中文翻译:
ap(x)$ p(x)$ -Laplacian Dirichlet问题的径向解的存在性
在本文中,使用变分方法,我们证明了广义\(p(x)\)- Laplacian问题的至少一个正径向解的存在
$$-\ Delta _ {p(x)} u + R(x)u ^ {p(x)-2} u = a(x)\ vert u \ vert ^ {q(x)-2} u- b(x)\ vert u \ vert ^ {r(x)-2} u $$在\(\ mathbb {R} ^ {N} \)(对于\(N \ geq 3 \))的单位球中具有Dirichlet边界条件,其中a,b,R是径向函数。