On the radial solutions of a p-laplacian equation involving a nonlinear gradient term and initial datum
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Keywords:
Elliptic equation, p-Laplace operator, radial solutions, positive solutions, gradient term, asymptotic behavior, shooting methodAbstract
The present paper establishes the existence, uniqueness and asymptotic behavior of positive radial solutions to the following ordinary differential equation with a positive initial datum
\begin{align*}
(|v^{\prime }|^{p-2} v^{\prime})^{\prime}+\dfrac{N-1}{r}|v^{\prime }|^{p-2} v^{\prime} +rv^{\prime } + v =0 \quad \text{ for} \ r>0,
\end{align*}
where $p>2$ and $N>1$.
We start by providing a result on the existence of radial positive solutions using the shooting method and an associated energy function. Next, we derived crucial findings regarding the behavior of entire solutions near infinity. More precisely, we prove that the solutions behave like the function $l/r$, where $l$ is a positive constant.
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