We study the existence of radial solutions for the p-Laplacian Neumann problem with gradient term of the type

$$\begin{aligned} \left\{ \begin{array}{l} -\Delta _{p}u=f(|x|,u,x\cdot \nabla u)\quad \text {in} ~\varOmega ,\\ \displaystyle \frac{\partial u}{\partial \mathbf{n} }=0\quad \text {on}~ \partial \varOmega , \end{array} \right. \end{aligned}$$

where \(\Delta _pu=\text {div}(|\nabla u|^{p-2}\nabla u)\) is the p-Laplace operator with \(p>1\), \(\varOmega \subset \mathbb {R}^N(N\ge 2)\) is a ball. We do not impose any growth restrictions on the nonlinearity. By using the topological transversality method together with the barrier strip technique, the existence of radial solutions to the above problem is obtained.

中文翻译：

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无增长约束的含梯度项的p-Laplacian Neumann问题的径向解

我们研究类型为梯度项的p -Laplacian Neumann问题的径向解的存在性

$$ \ begin {aligned} \ left \ {\ begin {array} {l}-\ Delta _ {p} u = f（| x |，u，x \ cdot \ nabla u）\ quad \ text {in} 〜\ varOmega，\\ \ displaystyle \ frac {\ partial u} {\ partial \ mathbf {n}} = 0 \ quad \ text {on}〜\ partial \ varOmega，\ end {array} \ right。\ end {aligned} $$

其中\（\ Delta _pu = \ text {div}（| \ nabla u | ^ {p-2} \ nabla u）\）是p -Laplace运算符，具有\（p> 1 \），\（\ varOmega \子集\ mathbb {R} ^ N（N \ ge 2）\）是一个球。我们不对非线性施加任何增长限制。通过结合使用拓扑横向方法和障碍带技术，可以获得上述问题的径向解。