论文标题
对数加权$ n $ -laplacian问题的鼻结解决方案与指数非线性问题
Nodal solutions for Logarithmic weighted $N$-Laplacian problem with exponential nonlinearities
论文作者
论文摘要
在本文中，我们研究以下问题$$ - {\ rm div}（ω（x）| \ nabla u |^{n-2} \ nabla u）=λf（x，x，x，u）\ quad \ mbox {in} $ \ mathbb {r^{n}} $，$ n \ geq2 $和$ w（x）$一个对数类型的单数重量。反应来源$ f（x，u）$是$ x $的径向功能，相对于指数类型的最大增长是亚临界或关键的。通过使用Nehari集合中的约束最小化以及定量变形引理和程度理论，我们证明了淋巴结溶液的存在。
In this article, we study the following problem $$-{\rm div} (ω(x)|\nabla u|^{N-2} \nabla u) = λ f(x,u) \quad\mbox{ in }\quad B, \quad u=0 \quad\mbox{ on } \quad\partial B,$$ where $B$ is the unit ball of $\mathbb{R^{N}}$, $N\geq2$ and $ w(x)$ a singular weight of logarithm type. The reaction source $f(x,u)$ is a radial function with respect to $x$ and is subcritical or critical with respect to a maximal growth of exponential type. By using the constrained minimization in Nehari set coupled with the quantitative deformation lemma and degree theory, we prove the existence of nodal solutions.
