Summary.
The paper deals with the existence of positive radial solutions for the p-Laplacian system div(|∇ u i |p-2∇ u i ) + f i(u 1, ..., u n ) = 0, |x| < 1, u i (x) = 0, on \(|x| = 1, i = 1, \ldots, n, p > 1, x \in {{\mathbb{R}}}^N\) . Here f i, i = 1,...,n, are continuous and nonnegative functions. Let \({\bf u}= (u_1, \ldots, u_n), \| {\bf u}\| = \sum^n_{i=1}|u_i|, f^i_0 = \lim_{\| u \|\rightarrow 0} \frac{f^i(u)}{\| {\bf u}\| ^{p-1}}, f^i_\infty = \lim_{\| {\bf u}\| \rightarrow \infty} \frac{f^i(u)}{{\|\bf u}\| ^{p-1}}, i = 1, \ldots , n, {\bf f} = (f^1, \ldots , f^n), {\bf f}_0 = \sum^n_{i=1} f^i_0\) and f ∞ = ∑n i=1 f i ∞. We prove that f 0 = ∞ and f ∞ = 0 (sublinear), guarantee the existence of positive radial solutions for the problem. Our methods employ fixed point theorems in a cone.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Manuscript received: June 20, 2005 and, in final form, July 2, 2007.
Rights and permissions
About this article
Cite this article
O’Regan, D., Wang, H. Positive radial solutions for p-Laplacian systems. Aequ. math. 75, 43–50 (2008). https://doi.org/10.1007/s00010-007-2909-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00010-007-2909-3